laboratory manual physics 1400 - al akhawayn …physics_lab/labman/phy1400_lab_manual.pdf ·...
TRANSCRIPT
1
School of Science & EngineeringSchool of Science & EngineeringSchool of Science & EngineeringSchool of Science & Engineering
LABORATORY MANUAL
PHYSICS 1400
Cours : Phy 1400
Semester : Fall 2008
By :
Dr.Khalid Loudyi
2
Table of contents:
INFORMATIONS AND INSTRUCTIONS FOR GENERAL PHYSICS LABORATORIES ...........3
PHYSICS LABORATORY RULES ...................................................................................................4
LABORATORY SUPPLIES & EQUIPMENT ...................................................................................5
The Experiments:
GRAPHS AND GRAPHICAL ANALYSIS........................................................................................6
THE MEASUREMENT OF MASS, LENGTH AND TIME ............................................................11
THE SIMPLE PENDULUM..............................................................................................................19
VECTORS AND EQUILIBRIUM.....................................................................................................25
WORK AND ENERGY IN THE SIMPLE PENDULUM ................................................................30
ELASTIC PROPERTIES OF DEFORMABLE BODIES .................................................................36
GAS LAWS ( BOYLE’S AND GAY-LUSSAC’S LAW) ................................................................40
BUOYANT FORCES........................................................................................................................46
THE FORMATION OF STANDING WAVES --MELDE’S EXPERIMENT .................................51
ELECTRIC FIELDS AND LINES OF FORCE.................................................................................56
GETTING FAMILIAR WITH THE OSCILLOSCOPE ....................................................................61
OHM’S LAW.....................................................................................................................................68
THE SIMPLE LENS..........................................................................................................................75
3
INFORMATIONS AND INSTRUCTIONS FOR GENERAL PHYSICS LABORATORIES
In science, no idea is accepted, no theory is believed, until they have been tested, then tested
again. Only then can the truth of the theory emerge. The ultimate test of any physical theory is by
experiment. This reliance on experiment differentiates science form other important human activities.
Unfortunately the beginning student often misses the importance of experiment to physics. Years or
centuries after the crucial experiments have been done; the student finds scientific truth by studying a
textbook. To show the student the importance of experiment in establishing "truth", we provide the
Physics Laboratory as part of your General Physics Course. The physical laws make predictions. We
do experiments to see if these predictions hold true, and, if they do, then, and only then, can we have
confidence in the truth of the laws.
The goal of any science is to arrive at a simple and universal explanation of natural events.
These explanations start out as theories, and they become physical laws if they are shown to be true by
comparing their predictions with the results of many experiments. Your experience in the physics
laboratory will, in a way, be similar to that of scientists in research laboratories around the world.
However, our laboratory differs form the research laboratories of professional scientists in that we
already know what theory will be applied to explain the experimental results. This means that you will
probably not discover any new physical laws this semester in the physics lab. However, you will learn
some of the methods of experimental physics used by scientists at the forefront of physics research.
While taking a physics laboratory; you will learn how to make scientific measurements and
how to present and understand these measurements by means of graphs and tables. You will also learn
the inherent limitations of measurements by discussing error analysis. These techniques can be
applied to problems in a large number of fields, other than physics such as the social, behavioural, and
life sciences.
Finally, we want you to enjoy yourself in the physics laboratory. Those of you who plan to
make a career of science will find it immensely satisfying to verify the predictions of a scientific
theory. We also hope that those of you who do not go on to become practicing scientists take with you
the excitement of "doing" physics.
4
PHYSICS LABORATORY RULES
The following suggestions will help you do your work in the physics laboratory:
1. Report to the laboratory promptly, ready to work. Expect to remain for the full lab period.
2. Your laboratory station should have everything you need to complete the lab assignment. If you
encounter a shortage (or damaged equipment), notify your instructor immediately. Never borrow
any apparatus from another station even though it may not be in use. At the end of the lab period,
check your station and leave it in good order. Again, call attention of the instructor to any
equipment problems you may have encountered. Space at the lab station is limited. You should
have only the laboratory manual and one or two sheets of clean scratch paper at your workstation.
Books, coats, hats, large purses, etc. should be stored elsewhere.
3. No food, drink, or tobacco in any form is permitted in the laboratory.
4. Each student working on his own conducts laboratory work.
5. The laboratory is a working area. Feel free to get up and stretch or go out for a drink of water. Talk
with your fellow students or your instructor. Consult your instructor when you have a question
about your work.
6. Do not waist time. Report to your work area, review the previous week's work and return it to the
instructor (5 minutes), and then get involved in the experiment activity. Do not wait for the
instructor to tell you what to do.
7. Be prepared before you come to the lab. Read the experiment as well as any helpful information
provided in the introductory portion of the laboratory manual before you attend lab. Failure to be
prepared will cause delays and you may not be able to complete the experiment in the allotted time.
8. Always keep your emphasis on quality of work and completeness of understanding. Do not set a
high priority on the amount of work accomplished in a laboratory period.
5
LABORATORY SUPPLIES & EQUIPMENT
This laboratory manual contains write-ups of experiments to be performed during the semester,
as well as materials explaining laboratory policies and generally accepted laboratory practices.
In addition to the laboratory manual, every student should bring the following supplies to
each lab session:
• One or two pencils (We prefer that you use pencil instead of pen in the laboratory.)
• A good eraser
• A combination straightedge and protractor.
• Bring your own calculator and DO NOT plan to borrow one from your laboratory partner
NOTE: We do not allow students to fail to buy these materials and then borrow them
from other students during the lab. There will be no need to carry your physics textbook to the
laboratory. The current experiment should be read before coming to each lab period.
6
EXPERIMENT 1
GRAPHS AND GRAPHICAL ANALYSIS
INTRODUCTION
In physics laboratories the student is often asked to make a graph of the data he has gathered, and
usually the graph is the technique by which the data is analysed. It is therefore important for the student to have a good idea of how to go about plotting a graph, and how a graph may be used to analyse (particularly, non-linear) data.
In this experiment you will: (a) learn to quickly, and accurately plot a graph. (b) Learn using graphical techniques to analyse laboratory data.
THEORY
1. What is to be plotted?
When the student is told to plot, say, S versus (vrs) t, it is accepted that this means: 1) S is the dependent variable, plotted on the "y" or vertical axis; and, 2) t is the independent variable, to be plotted on the "x" or horizontal axis. This is a convention (agreement) which should be memorised.
2. Choice of Scale.
The scale of a graph is the number of (usually) centimetres of length of graph paper allotted to a unit
of the variable being plotted. For example, 1 cm for each 10 seconds of time. In general the scales for the x and y axes may be different.
There are two criteria for choosing the scale of a graph, range of the variable, and convenience in
plotting:
a) range of the variable: Suppose the range of values of S is from 5 cm to 125 cm. We then need a scale for S that allows us to plot values from 0 to values somewhat greater than 125 cm. Notice that (unless told to do so by the instructor) we do not choose to suppress the zero of the graph and start the S scale from 5 cm. The reason is that we may later need to use the graph to find values extrapolated (continued) to the zero.
Also we usually try to allow space on the graph for values somewhat greater than the largest value (in this example, 125 cm) because we may take a little more data in the experiment, with larger values, or we might want to extrapolate the graph to larger values.
Finally the scale should be chosen to most nearly use the whole of the graph paper. Just because a choice of, say, l cm to represent 1 sec of time makes the graph easy to plot, we should not do this if it makes the graph only occupy a small part of the whole paper and be hard to read and use. b) Convenience in Plotting: It turns out (as we shall see in an exercise in this lab) that scales of 1, 2, 5, and 10 (and multiples of 10 of these) per centimeter are easiest to use; a scale of 4 per centimeter is somewhat more difficult, but can be used; but scales of 3, 6, 7 , 9, etc.. per centimeter are very difficult and should be avoided. In choosing scales it sometimes helps to turn the paper so that the "x-axis" is either the long or short dimension of the paper.
3. Label the Axes and put a title to the graph
The vertical and horizontal axes of the paper should carry labels of the quantities to be plotted, with units. In our previous example the label on the y-axis would be: S(cm). The graph itself should have a title. In our example the title is: Plot of S vrs t.
4. Circle your Data Points
7
Each data point should have a neat circle drawn around it. If more than one experimental trial is used one can use circles, triangles, squares, with a legend to distinguish these.
5. Put a Smooth Solid Curve through the Data Points
This can be done "by hand" or with a plotting aid. Ignore any points which fall far outside the curve
(after checking that they are plotted correctly). A dashed line should indicate extrapolations to larger or
smaller values, outside of the range of data taken.
6.Graphical Analysis
Often we have data (x, y) which we believe follows the theoretical relation y = rnx + b; we can verify
this relation if we obtain a straight line when we plot y vrs x. Also, the plot obtained allows us to find the
values of m and b as follows: b = y-intercept of graph (value of y when x = 0) m = slope of graph = ∆y/∆x = (Y2-Y1)/(X2-X1 )
Other times we have data which we believe follows a non-linear theoretical relation. For example consider S = (1/2)at². We can verify this relation by plotting S vrs t². If this relationship holds then the graph will be a straight line with intercept zero. The slope of the graph then gives the constant a/2. remarks: The points chosen to determine the slope should be relatively far apart. Points corresponding to data points should not be chosen, even if they appear to lie on the line.
EXPERIMENTAL PROCEDURE
Exercise 1.
Consider the following data:
S (m) 0.27 1.08 2.43 4.32 6.75 9.72
t(sec) 0.10 0.20 0.30 0.40 0.50 0.60
• On a sheet of graph paper draw 5 lines parallel to the y-axis, each separated by a few centimeters. Plot
the values of S on the 5 lines to the following scales (with some scales you may not be able to plot all points):
a) 1 m equivalent to l cm.
b) 1 m equivalent to 2cm.
c) 1 m equivalent to 3cm.
d) 1 m equivalent to 5cm.
e) 1 m equivalent to 7 cm.
• Which scales are easy to plot?
• Which scales are difficult? Explain why.
Exercise 2.
Y (units)
X (units)
(x1, y1)
(x2, y2)
∆x
∆y
y-intercept
y = mx + b
8
• Plot a graph of S vs t.
• Does this plot give a straight line?
Exercise 3.
• On the same graph paper as for exercise 2, plot a graph of S vrs. t². This should give a straight-line plot.
• What is the y-intercept of this graph?
• What is the slope of the straight line? (Include units.)
Conclusion:
Conclusions are a necessary part of every experiment. The main purpose of the conclusions is to
summerize the following:
• What was investigated? ie. relate to how the purpose was confirmed or contradicted. What was found?
ie. outcome of graphs and main qualitative/quantitative results • What can be interpreted? ie. significance of graphs/results and correlation to theory • Lastly, you would discuss reasons for any serious discrepancy and any major problems encountered in
the experiment (and perhaps suggestions for improvement). When comparing experimental results to expected values, it is important to quote the result together with its associated uncertainty (error). If the difference between experimental and expected values is greater than the expected uncertainty, you should note the disagreement and give possible reasons for the discrepancy (sources of errors). If the experiment deviates from theory, then you can try to explain the deviation, or perhaps, modify the theory to account for the behavior. For example, theory often assumes idealized conditions, but in the actual experiment these ideal conditions may not be true.
9
EXPERIMENT 1
GRAPHS AND GRAPHICAL ANALYSIS
NAME: . DATE: .
SECTION: .
* * *
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points) Answer Pre Lab Question:
PHY 1400 LABORATORY REPORT
10
3. RESULTS AND ANALYSIS
Exercise 1:
Graphs of S with different scales in attached graph paper: (15 points)
Questions (15 points)
Exercise 2 :
Graph of S vrs. t in attached graph paper: (20 points)
Questions (5 points)
Exercise 3:
Graph of S vrs. t² in attached graph paper: (15 points)
Questions (10 points)
Conclusions: (10 points)
11
EXPERIMENT 2
THE MEASUREMENT OF MASS, LENGTH AND TIME
INTRODUCTION:
The purpose of this experiment is to familiarise you with the basic measurement necessary to
make physical observations. The procedures outlined illustrate the difference between basic physical
quantities(e.g. mass, length and time) and derived quantities (e.g. volume, area and density). The
units used to describe these quantities are also introduced, and appreciation of the methods and
accuracy by which these quantities can be measured.
BACKGROUND:
Physics is fundamental an observational science. All “laws”, ”theories”, ”principles”, ...etc.
are based upon experimental observation. We observe nature, and then devise laws and theories,
...etc. to explain our observations. We then test our theories by using them to predict what will
happen given a certain set of conditions. We set up those conditions in experiments and in this way
make further observations that either support or deny our original theory. It becomes clear then that a
fundamental aspect of physics is the ability to make accurate observations. The observations
themselves usually consist of detailed measurements. Often, our theories stand or fall based on the
accuracy with which we can make these measurements.
The quantities length , mass and time are the so-called base quantities in mechanics; their
corresponding units are called the base units. The word base refers to the fact that they cannot be
defined in terms of any other quantities or units; they are fundamental “building blocks” of all other
quantities. That is all other quantities can be defined in terms of mass, length and time. These latter
quantities are called derived quantities and the corresponding units are derived units.
As a simple example, the derived quantity density is defined in terms of the base quantities
mass and length, thus:
Density = Mass/Volume
or, similarly, speed is derived thus:
Speed = Distance/Time
Thus, the accuracy with which density (for example) can be measured depends upon the accuracy
with which length and mass can be measured.
THE EXPERIMENT:
1- Experimental Apparatus:
The apparatus for this experiment consists of: plastic ruler, meter stick, electronic balance,
Ohaus balance, pair of callipers, micrometer gauge, graduated cylinder, stopwatch, and a variety of
objects for measurement.
2- Experimental Procedure:
A. Measurements of Regular Shaped Objects
a) Steel cylinder measurements using meter stick and pan balance:
12
• Measure the length and diameter of the steel cylinder using the meter stick record the result in the
data table in your laboratory report. You should make the measurement several times and then
compare results - this is one of the best way to avoid careless results in the laboratory work.
• Measure the mass of the cylinder using the pan (Ohaus) balance.
• Calculate the volume of the steel cylinder. The volume of a cylinder is the product of its height
(h) and its cross-sectional area, namely:
V h r= π 2
where r is the cylinder’s radius.
• Calculate the density of the steel cylinder in the space provided and record your answer in the
table. SHOW YOUR WORK, showing the correct use of units and significant figures.
The density of the cylinder is then its mass (M) divided by its volume:
ρ =M
V
b) Steel cylinder measurements using vernier calliper and electronic balance:
Another useful instrument for measuring length is the vernier calliper, shown schematically in Fig 1
FIGURE 1: A vernier calliper,
• Take several readings of the length and diameter of the cylinder with the vernier calliper. When
you are satisfied with your answer, record the data in the second row of the table.
• Now use the electronic balance to measure the mass of the cylinder.
• Recalculate the volume and density and show your work in the appropriate section of your
laboratory report.
c) Steel sphere measurements using vernier calliper and electronic balance:
13
• Measure the diameter of the sphere with the vernier calliper. When you are satisfied with your
answer, record the data in the third row of the table.
• Measure the mass of the sphere by using the electronic balance.
• Calculate the density of the steel sphere. Note that the volume of a sphere is given by:
V r=4
3
3π
where r is the radius of the sphere.
d) Steel sphere measurements using micrometer and electronic balance:
The micrometer calliper is an instrument used for the accurate measurement of short lengths (see
Figure 2).
FIGURE 2: A micrometer calliper
• Measure the diameter of the steel ball using the micrometer and record it on the fourth row of
Table I.
• Calculate the density of the steel ball.
• Compare this measurement with those that you’ve made earlier.
B. Measurements of Irregular Shaped Objects
The above measurements were straightforward because of the regular shape of the objects
concerned. The volumes of these objects were easy to calculate using prescribed formulae. However,
what about irregular shaped objects, such as the rock provided in this experiment? To calculate the
volume of such objects is difficult, if not impossible. To determine the density thus requires a
separate measurement (i.e. not a calculation) of the volume. To do this proceed by:
• Measuring the mass of the rock using the electronic balance.
• Fill the graduated cylinder about half-full of water and note the level to which the water rises in
the cylinder. Fully immerse the rock fragment in the water, and note the new water level.
Subtraction of two readings gives the volume of the rock..
• Calculate the rock’s density. Show all your data and your calculations in the space provided in
the laboratory report.
C. Time Measurements
14
• Familiarise yourself with the operation of the stopwatch. Experiment to determine the shortest
time interval that you can measure.
• Construct a ramp by taping one end of the plastic ruler and elevating one end by about 1/4 of an
inch. -use a pencil or a thin notebook.
• Let the steel ball roll down the ramp and on to the table, and determine the time taken for the ball
to roll over a distance of 1 m on the table. Record your results in the data table.
• Repeat the measurement three times and determine the average time value.
• From this calculate the average speed of the ball
The average speed, defined as:
average speed = length traveled
time taken
D. Percent Difference and Errors
a) If you have measured the same quantity more than one-way, one can calculate the percent
difference between the two results. This is defined as:
100tsmeasuremen twoof average
tsmeasuremen twobetween differencedifference% x=
• Calculate the percent difference in the two values you obtained for the density of the steel
cylinder, the values obtained in row 1 and row 2 of the data table I.
b) If a “true” or reference value is known for the measured quantity, one calculate a percent error for
the experimental result, thus:
100 valuereference
valuereferencevalue alexperimenterror% ×
−=
• Calculate the percent error in your experimental value for this quantity (use the value obtained in
row 4 of the data table I). Assume the reference value for the density of steel as 7.8 g/cm3.
• List reasons (other than measurement errors) why your measured value for the density of steel
may differ from the accepted value.
c) The smallest sub-division marked on a measuring instrument is sometimes called the least measure
of the instrument.
• List the measuring instruments used in this experiment and note their least measure.
d) When making experimental measurements one can also expect error due to imprecision in the
measurement. Thus one defines:
100measured quantity theof magnitude
instrument the of measureleast error expected ×=
• Calculate the expected errors for the diameter of the steel cylinder using the meter stick, and using
the vernier callipers. Also calculate the expected error in the measurement of the diameter of the
steel sphere using the micrometer gauge.
15
EXPERIMENT 2
THE MEASUREMENT OF MASS, LENGTH AND TIME
NAME . DATE: .
SECTION: .
THIS ¨PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB.
SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points )
Briefly outline the apparatus
General procedures adopted.
PHY 1400 LABORATORY REPORT
16
3. RESULTS AND ANALYSIS
A. Measurements for Regular Shaped Objects
Data (15 points )
Data Table I: Density of Selected Solids
Object Measured Measuring
Instrument
Length
(cm)
Diameter
(cm)
Mass (g) Volume
(cm3)
Density
(g/cm3)
Steel Cylinder Meter Stick
Steel Cylinder Vernier Calliper
Steel Sphere Vernier Calliper
Steel Sphere Micrometer
Calculations Show your work
Volume of cylinder (using meter stick) (5 points)
Density of cylinder (using meter stick ) (5 points)
Volumes of cylinder and steel ball (using vernier-callipers ) ( 5 points )
Densities of cylinder and steel ball (using vernier-callipers ) ( 5 points )
Volumes and Densities of steel ball (using micrometer ) ( 5 points )
17
B. Measurements for Irregular Shaped Objects: Rock (10 points)
Volume of water (before rock immersed):
Volume of water (after rock immersed):
Volume of rock:
Mass of rock:
Density of rock:
C. Time measurements
Table 3 (5 points )
Average speed calculations: (5 points)
18
D. Percent Difference and Error
a) Density of steel; percent difference (5 points)
b) Density of steel; percent Error (5 points)
Reasons for percent difference and percent error (5 points)
c) Least Measures (5 points )
d) Expected Errors (5 points)
19
EXPERIMENT 3
THE SIMPLE PENDULUM
INTRODUCTION
The simple pendulum offers a method of measuring the constant acceleration due to gravity
very precisely. The object of this experiment is to study simple harmonic motion of the simple
pendulum and to measure the acceleration of gravity g.
THEORETICAL BACKGROUND
A simple pendulum is defined, ideally, as a particle suspended by a weightless string.
Practically it consists of a small body, usually a sphere, suspended by a string whose mass is
negligible in comparison with that of the sphere and whose length is very much grater than the radius
of the sphere. Under these conditions, the mass of the system may be considered as concentrated at a
point -namely, the center of the sphere- and the problem may be handled by considering the
transitional motion of the suspended body, commonly called “bob,” along a circular arc.
Figure 1: Diagram Analysis of the Simple Pendulum.
Consider the diagram of a simple pendulum shown in Figure 1. When the pendulum is
released from a given displacement, it moves with increasing velocity toward its equilibrium position.
Note that if angle θ is small, sin θ is very nearly equal to the displacement, arc length x. This
displacement is described by:
x A t= sinω (Eq. 1)
where ω is the angular velocity. The period of vibration is the time required for it to go through one
cycle (i.e., the time for pendulum to move from any point on its path back to the same point with
motion in the same direction), and is related to ω by the relation T = 2π/ω.
Tl
g= 2π (Eq. 2)
20
Note finally that the constant A in Equation (1) is the amplitude of the motion which measures
how far the bob swings away from the vertical -the maximum value of the displacement. This is
conveniently expressed as an angle in degrees.
THE EXPERIMENT:
After you read the preceding material, you may notice that among the factors that might affect
the period of a simple pendulum are the mass of the pendulum, the length of the pendulum, and the
amplitude of its swing. We shall confine our attention to these as they are easy to control
experimentally.
If we are to investigate the effect of any one of these variables on the period of the pendulum,
the remaining variables must be controlled (i.e., they must not be allowed to change during the
experiment). Suppose we start with an investigation of the effect of length upon the period. This
means that we choose a pendulum of fixed mass, allow it to swing always through angles of the same
amplitude, and observe changes in the period due to changes in the length of the pendulum.
1. EXPERIMENTAL APPARATUS:
The experimental apparatus consists of rods, clamps, pendulum bobs, string, metric ruler, stop
watch, protector, electronic balance, computer, the Lab Pro interface, Lab Pro software and the
Motion Detector.
1. EXPERIMENTAL PROCEDURE:
A. Effect of changing length on the pendulum period:
• Prepare a pendulum about 1 m long.
• Position the Ultrasonic Motion Detector so that it monitors the motion of the pendulum.
Remember that the pendulum must be placed at more than 0.5 m distance away from the
motion detector. Use the computer to measure the position of the ball versus time. To do this make sure the motion sensor is
plugged into the Lab Pro device and the Lab Pro’s USB cable is plugged into the computer.
Open Logger Pro using the icon on the desktop.
Logger Pro should automatically recognize the sensors, if it doesn’t:
Click on LabPro icon, a window will open with a picture of the LabPro. Select the Dig/Sonic 1 box in the
upper right hand corner and choose the Motion Detector
You can close the LabPro window now.
• Give the mass a small displacement from equilibrium (around 5 degrees), let it swing within the
range of the motion detector, and click the Collect button to start the data collection. Make sure
that the time period for data collection is long enough to accommodate at least ten periods (use
the timer icon) of the pendulum swing.
• Repeat this step until you obtain a good data set.
• While you are taking these computerized data acquisitions, you should use the provided stop-
watch to measure the time for the ten periods of the pendulum oscillations. This period can be
determined with greater accuracy if the time to make a large number of cycles (say 10) is noted
and the period calculated by dividing the total time by the number of cycles.
• Record the mass, amplitude, length, and period of the pendulum in Data Table 1.
• Decrease the length of the pendulum by about 15 cm and determine the period in the same
manner, and record the results in data Table I.
• Repeat the measurement for total 5 lengths of the pendulum, the last length should be about 20
cm, and record the results in data Table I.
Remember that both the mass and the amplitude must remain the same throughout this series
of observations.
21
B. Effect of changing mass on the pendulum period:
• Prepare a pendulum about 75 cm length.
• Change the mass while holding the length and the amplitude constant. Displace the mass at a
small angle (around 5 degrees).
• Use the stop-watch to measure the time for the ten periods of the pendulum oscillations.
• Record the period of oscillation in data table II.
• Repeat the same procedure for three different masses, and report the results in data table II.
C. Effect of changing amplitude on the pendulum period:
• Prepare a pendulum about 75 cm length.
• Change the amplitude while holding the length and the mass constant. To start displace the mass
at a small angle (around 5 degrees).
• Use the stop-watch to measure the time for the ten periods of the pendulum oscillations.
• Record the period of oscillation in data table III.
• Repeat the same procedure for three different amplitudes (not to exceed 30 degrees), and report
the results in data table III. Keep the length and the mass constant.
DATA ANALYSIS:
• Using the data collected in Table I, prepare a graph of the period versus the length of the
pendulum.
• On the same sheet of graph paper, plot a graph of T² versus L (This required a different vertical
scale since a different quantity is being plotted). To avoid the confusion, place the new scale
along the right margin of the graph paper.
• Explain the relationship between the length and the period.
• Summarise the results of your three experiments. Examine your data and graphs carefully before
writing.
• Using graphs of T² vrs. L, calculate the experimental value of g.
• Show your calculation on the worksheet. Compare your calculated g value to the theoretical
value of 9.8 m/s².
22
EXPERIMENT 3
THE SIMPLE PENDULUM
NAME: . DATE: _____________________ .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB.
SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment (5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points )
Briefly outline the apparatus
General procedures adopted.
PHY 1400 LABORATORY REPORT
23
3. DATA and ANALYSIS:
TABLE 1: (15 points)
Length, L Time for 10 cycles Period, T T²
LoggerPro Stop watch LoggerPro Stop watch LoggerPro Stop watch
TABLE 2: (10 points) TABLE (10 points):
Graphs (20 points)
Summary of the graphs: (5 points)
Summary of three experiments: (10 points)
24
Calculations of “g”: (5 points)
Comparison between theoretical value and experimental result of “g”, Percent error:(5 point)
CONCLUSIONS: (10 points)
25
EXPERIMENT 4
VECTORS AND EQUILIBRIUM
INTRODUCTION:
The purpose of this experiment is to confirm the laws of vector addition, and to study the
equilibrium of force vectors at a point.
BACKGROUND:
A scalar is a quantity that has magnitude only; examples are temperature, mass, and density.
A vector is a quantity that has both magnitude and direction; examples are velocity, acceleration, and
force.
A vector may be represented by a straight line in the direction of the vector, with the length of
the line proportional to its magnitude. Placing an arrowhead at the end of the line indicates the
direction of the vector.
Vectors may be added. The sum or resultant of two or more vectors is defined as the single
vector that produces the same effect. Figure 1 shows the resultant of two forces A and B.
The resultant is defined as the force equal and opposite to the resultant as shown in Figure 1.
If the resultant is added to the sum of A and B the sum of the forces equals zero, and the system of
forces is in equilibrium.
Vector addition may be accomplished graphically or analytically. Using the graphical method
for more than two forces we have the polygon method of vector addition: the vectors to be added are
placed so that the tail of the second is on the head of the first vector, maintaining their original
directions. The tail of the third vector is placed on the head of the second vector, etc. when all the
vectors are in place, the side which closes the polygon is the resultant of the vectors. This is shown in
figure 2, for the addition of vectors A, B, C, and D. If the polygon closes by itself, the resultant is
equal to zero and the vectors, if representing forces, are in equilibrium.
Equilibrant
Resulant
A
B
A
B R
Figure.3: Polygon
method for addition of
two vectors A, B
Fig. 4. The Parallelogram
method to add two vectors A,
B
180
270
90
0
Resultant
A
B
Figure 1: The resultant and
equilibrant of two forces A, B.
A
B
C
D
R
Figure 2: Polygon method to add
four vectors A, B, C, D.
26
Then addition of the two vectors is most conveniently carried out by the parallelogram
method shown in figure 4.
Vectors may also be added analytically, and this is preferred to the graphical method since
one does not have to make precise drawings. The method is illustrated in figure 5 for the addition of
two vectors A and B. The vectors are broken down into components:
then R = Rx i + Ry j where Rx = Ax + Bx, and Ry = Ay + By
The magnitude of R is then
R = (Rx² + Ry²)1/2 = [(Ax + Bx)² + (Ay + By)²]
1/2
while the angle that R make with the x-axis is given by
θ = tan-1(Ry/Rx) = tan-1[(Ay + By) / (Ax + Bx)]
This method may be extended easily to the sum of any number of vectors A, B, C, etc. by just
replacing the appropriate quantities in equations (1) and (2) by sums of all the x and y components.
THE EXPERIMENT:
1- Experimental Apparatus:
Vectors and the equilibrium of forces may be most easily studied in the lab by means of the
force table shown in figure 6. The apparatus consists of: force table, weight hanger, slotted weights,
ring attached to strings, and pulleys.
θθθθA
R
A
B
θθθθB
θθθθ
iAx Ax Bx
Ay
By
y
x
Figure 5. Analytic addition of two vectors A, B
A = Ax i + Ay j
B = Bx i + By j
where
Ax = A cos θA Ay = A sin θA
Bx = B cos θB By = B sin θB
(1)
(2)
Figure 6: Force Table
27
2- Experimental Procedure:
Part A
• Mount a pulley on the 30° mark and suspend a total of 200 g over it. By means of a vector
diagram drawn to scale (choose your own scale) find the magnitude of the components along the
0° and 90° directions.
• Set up on the force table 0° and 90° forces you found from the diagram. These forces are
equivalent to the original force. Test this statement by replacing the initial force at 30° by an
equal force at 180° away from the initial direction, and check for equilibrium.
• Have your instructor check the equilibrium
Part B
• Mount a pulley on the 20° mark on the force table and suspend a total (including the mass holder)
of 100g over it. Mount a second pulley on the 120° mark and suspend a total of 200 g over it.
• Draw a vector diagram to scale, using a scale of 20 g per centimetre, and determine graphically
the direction and magnitude of the resultant using the parallelogram method.
• Check your results so far by setting up the resultant on the force table. Putting a pulley 180° from
the calculated direction of the resultant, and suspending weights equal to the magnitude of the
resultant does this.
• Have your instructor check the equilibrium
Part C
• Mount the first two pulleys as in Part B, with the same weights as before.
• Mount a third pulley on the 220° mark and suspend a total of 150 g over it.
• Draw a vector diagram to scale and determine graphically the direction and magnitude of the
resultant, (Hint: This may be done by adding the third vector to the sum of the first two, which
was obtained in Part A.) Now set up the resultant on the force table and test it as before.
ANALYSIS:
2. Calculate analytically the magnitude and direction of the resultant in part B and compare to the
graphical determination.
28
EXPERIMENT 4
VECTORS AND EQUILIBRIUM
NAME: . . DATE: . .
SECTION: . .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB.
SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS:
Briefly outline the apparatus used and the general procedures adopted. (5 points )
PHY 1400 LABORATORY REPORT
29
3. DATA and ANALYSIS:
Part A (20 points)
Attach the graphs and the analysis
Part B (25 points)
Attach the graphs and the analysis
Part C (25 points)
Attach the graphs and the analysis
ANALYSIS: (20 points)
30
EXPERIMENT 5
WORK AND ENERGY IN THE SIMPLE PENDULUM
INTRODUCTION:
Conservation laws play a fundamental role in modern physical theory. A conservation law is a
statement that there is some property of a system, such as energy, that does not change as we study the
system in a specified way. In this experiment, we seek to verify the law of conservation of energy for
a particular, simple system.
THEORY:
When a constant force, F, acts on an object, O, and results
in a displacement, x, the work done (W) is defined as the
product of force and displacement. Since both force and
displacement are vectors, the product must be found by using
not F but rather the component of the force in the direction of
the displacement; i.e., Fx in the direction of x (x being the
displacement).
W = (Fx)(x)
When an object of mass m is raised a vertical distance h=hf - hi
(hf being the final height and hi being the initial height of the
object) in the earth’s gravitational potential field, the
gravitational potential energy of the object changes by an
amount
GPE = mg (hf - hi )
where g is the acceleration due to gravity.
An object moving with speed, v, has kinetic energy (KE) associated with it given by the relation:
KE = mv²/2
We would also like to introduce the concept of the work-energy theorem which states that
when forces act on a body while it undergoes a displacement, the total work Wtot done on the object by
all the forces equals the change in the particle’s kinetic Energy, namely
Wtot = KE2 - KE1
Finally, the work done on an object in a uniform gravitational
field can be represented in terms of a potential energy (GPE) as:
Wgrav = mgy1 - mgy2 = GPE1 - GPE2
THE EXPERIMENT:
1. EXPERIMENTAL APPARATUS:
The apparatus used in this experiment is a pendulum with a
spherical bob. A string is fastened to the pendulum bob and passes
over a pulley to a weight hanger so that a known horizontal force can
x0 x1
F
Fx
x
hf
hi
Bob
Pulley
Load hi
hf
xi
xf
31
be applied to displace the pendulum. A timing device (photo-gate
timer), allows you to measure the speed of the pendulum as it passes
through the rest position. The units of work in the SI system are Joules (J)
2. EXPERIMENTAL PROCEDURE:
A. Measurement of the Work Done in Displacing the pendulum:
• Measure and record the mass of the pendulum bob.
• Construct a pendulum from the provided bob and strings. Allow the pendulum to hang vertically
and place the meter stick on the table with one end directly under the pendulum bob. The meter
stick should lie along the direction of the string be used to displace the pendulum. This string
should go over the pulley placed on the lab-table edge.
• Record hi, the initial height above the table of the string fastened to the pendulum bob (measure to
the center of the bob).
• Add the weight hanger to as a load to displace the pendulum bob. The string which displaces the
pendulum should be kept horizontal (parallel to the lab-table) by adjusting the height of the pulley
• Record the horizontal displacement of the pendulum bob form its initial position in the data table
of your lab-report.
• Add 10-gram mass to the weight hanger, make sure the string is horizontal by adjusting the height
of the pulley, and record (in the data table of your lab-report ) both the load (in Newtons) and the
horizontal displacement of the bob form its initial position.
• Repeat for a series of at least 10 different loads on the weight hanger (not to exceed 150 grams for
the final load), and record both the load and the horizontal displacement of the bob form its initial
position.
• For the largest load only, record the final height hf of the string attached to the pendulum bob.
• Draw a graph of Fx versus x.
• Find the work done on the pendulum by measuring the area under the curve of Fx versus x.
B. Measurement of Gravitational Potential Energy of the Pendulum:
• Calculate the increased gravitational potential energy of the pendulum bob in the elevated
position (refer to the Figure for further clarifications). Show your work.
C. Measurement of the Kinetic Energy of the Pendulum:
• Position the U-shaped arm of the photo-gate timer such that the pendulum bob hangs directly in
its center when the pendulum is at rest. During subsequent motion, the cylinder must interrupt the
light beam between the U-shaped arms to activate the timer.
• With the pendulum held at an elevated position hf turn on the timer (use the “gate” setting), and
release the mass of the pendulum from this elevated position, it will pass through the rest hi
position (i.e., equilibrium) with a kinetic energy of mv²/2. CAUTION: The attached string can
also trip the timer as it falls through the beam, consider only the time for the pendulum itself to
pass through the beam.
• In your lab-report record the beam-interruption time, which corresponds to the time for the
diameter of the bob to cross the photo-gate timer.
• Repeat the measurement as necessary to insure accuracy of the time (at least four measurements).
• Measure the diameter of the pendulum bob (sphere).
• Using this mass and the average photo-gate time calculate the velocity at the lowest point of the
pendulum swing.
• Calculated the maximum kinetic energy. Report your results in the lab-manual.
• In a brief paragraph, summarise the results of your experimental work.
• Calculate percent differences (between KE and W, KE and GPE, GPE and W). What does this
tell you about the meaning of work done by the variable force? How does this demonstrate
32
conservation of energy? Try to account for any significant difference between your results and
what you would expect to occur.
33
EXPERIMENT 5
WORK AND ENERGY IN THE SIMPLE PENDULUM
NAME: DATE: .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB.
SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS:
Briefly outline the apparatus used and the general procedures adopted. (5 points )
PHY 1400 LABORATORY REPORT
34
3. DATA and ANALYSIS: (10 points)
Mass of pendulum bob =
Initial height of string =
Final height of string =
TABLE 1: (20 points)
Attach graph of Fx versus x (20 points)
3. CALCULATIONS:
A.Work: (5 pints)
B. GPE: (5 points)
C. KE: (10 points)
35
4. SUMMARY OF RESULTS: (5 points)
Percent differences: (5 points)
%difference (Work and KE)
%difference (Work and PE)
%difference (PE and KE)
5. CONCLUSION: (10 points)
36
EXPERIMENT 6
ELASTIC PROPERTIES OF DEFORMABLE BODIES
INTRODUCTION:
In this experiment we have two goals. Firstly, we examine a rubber strap and a steel spring to
see if Hook’s law is obeyed and, if so, determine the constant of proportionality in the law. This
constant is frequently referred to as the “spring constant” or as the “force constant”. Secondly, we
investigate the energy transformation which occur when a mass is suspended from an elastic spring
and set into vertical oscillation.
THEORY
In 1678, Robert Hook announced his theory of elastic bodies.
Now known as “Hook’s law”, the theory states that the stretch (∆y) in
a wire or spring supporting a load (∆F) is directly proportional to the
load, or ∆F= k(∆y) where k is a proportionality constant
Elasticity:
Elasticity is the property of an object determining the extent
to which it tries to return to its original shape and size after removal
of a deformable force. In general the deformation of an object
increases as the applied force increases. If the deformation is directly
proportional to the applied force, we say the object obeys Hook’s law.
For the case of a linear stretching of an elastic material, we
may write Hook’s law in the form: F = kY, where F is the deforming
force, Y is the deformation of the material from its original size, and
the proportionality constant k is called the force constant. The graph
of this equation (F vrs. y) is a straight line and the slope is the force
constant, k.
Elastic Potential Energy:
The force-displacement curve for a body that obeys Hook’s
law is a straight-line, as shown. When the body has been stretched by
an amount y1 the force is ky1. The area under the F(y) curve
represents the work done. In this case,
ELASTIC ENERGY IN SPRING = KY²/2 (2)
THE EXPERIMENT: 1. EXPERIMENTAL APPARATUS:
To carry this experiment you lab station should have the following items: spring, rubber band,
mass hanger, slotted weights, meter stick, ruler.
2. EXPERIMENTAL PROCEDURE:
• Support the spring and meter stick as shown in
Figure 3.
y1
F
y
Work
Figure 2
ky
37
• Record Po (the location of the bottom of the spring when no load is applied).
• Add a weight hanger and record the new equilibrium
position.
• Fill up the cells of Table 1 in your laboratory report with
the data corresponding to mass increments of 20 g for the
spring.
• Change the spring with the rubber band and follow the
same procedure for recording the bottom of the band when
no load is applied, when the mass hanger is added, and
when new mass in increments of 200 g is added.
• Record the data in the corresponding cells of Table 1 of
your laboratory report.
ANALYSIS OF RESULTS:
• From the data collected in Table 1, plot a graph of the load-versus-displacement for the
spring and the rubber band. The graph paper is provided on the worksheet. Use the same
sheet for both graphs. Use the combination of right/lower axis for the spring data and the
left/upper axis for the rubber data.
• From the plotted data determine whether or not the steel spring and the rubber tube at your
lab station obey Hook’s law as expressed in equation (1).
• Determine the force constant, if it is appropriate. Briefly summarise the results of your
work.
38
EXPERIMENT 6
ELASTIC PROPERTIES OF DEFORMABLE BODIES
NAME: . . DATE: . .
SECTION: . .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB.
SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.(5 points)
2. EXPERIMENTAL PROCEDURES AND APPARATUS:
Briefly outline the apparatus used and the general procedures adopted. (5 points)
PHY 1400 LABORATORY REPORT
39
3. DATA and ANALYSIS:
TABLE 1: (25 points)
SPRING RUBBER
ADDED MASS POSITION ADDED MASS EQUILIBRIUM
GRAPH: Attach the graph(35 points)
Summary of graph: (10 points)
Spring Constant k calculation: (10 points)
4. CONCLUSIONS: (10 points)
40
EXPERIMENT 7
GAS LAWS ( BOYLE’S AND GAY-LUSSAC’S LAW)
INTRODUCTION:
In order to specify fully the condition of a gas it is necessary to know its pressure, volume,
and temperature. These quantities are interrelated, being connected by the general gas law, so that if
any two of them are known, the third is determined by the mathematical relation between them.
One of the important properties of a gas is that it always tends to expand until it completely
fills the vessel in which it is placed, and thus the pressure it exerts depends on the volume it occupies.
To describe fully the condition of a gas it is necessary to give not only the volume but also the
temperature and pressure, because they are all interrelated.
The purpose of this experiment is to study two of the gas laws; that is, to develop the
relation between the volume and the total pressure of a given mass of gas when the temperature is
kept constant; and to investigate the variation of the pressure, of a given mass, of gas with changes in
its temperature, when the volume is kept constant.
the volume to the pressure, and the pressure to the temperature.
THEORY
In studying the behaviour of a gas under different conditions of pressure, temperature, and
volume, it is convenient to keep one of these constant and to vary the other two. Thus, if the
temperature is kept constant, one obtains the relation between the pressure and the volume; if the
volume is kept constant, one gets the relation between the temperature and the pressure.
Boyl’s law: if the temperature is kept constant, the volume of a given mass of gas varies
inversely as the pressure. This means that for a constant temperature, the product of the volume and
the pressure of a given amount of gas is constant. Thus
PV = constant
(Eq. 1)
or P1V1 = P2V2, where V1 is the volume of a given mass of gas at pressure P1, and V2 is the volume at
pressure P2.
The experimental test of Boyl’s law consists in observing a series of different volumes,
measuring the corresponding pressures, and observing how nearly constant the product of the two
remains.
GAY-LUSSAC LAW: if the volume remains constant, the pressure of a container of a gas is directly
proportional to its absolute temperature.
THE EXPERIMENT:
1. EXPERIMENTAL APPARATUS:
To demonstrate the concept of BOYL’S LAW (pressure vs. volume) and GAY-LUSSAC’S
LAW (pressure vs. absolute temperature) you will use the Pressure Sensor and the temperature
Probe with the Vernier Logger Pro Software and its Interface (Lab Pro). You will also find your
laboratory station equipped with an Erlenmeyer flask, beaker, and heating plate.
3. EXPERIMENTAL PROCEDURE:
41
The white stem on the end of the Gas Pressure Sensor Box has a small threaded end called a luer
lock. With a gentle half turn, you may attach the plastic tubing to this stem using one of the
connectors already mounted on both ends of the tubing. The Luer connector at the other end of the
plastic tubing can then be connected to one of the stems on the rubber stoppers that are supplied, as
shown in figure 1.
Figure 1 Figure 2 Figure 3
Preparing Logger Pro for Measurements
A. Boyl’s law experiment:
• Connect the Pressure Sensor into the LabPro interface's Ch.1; Open the LoggerPro application
from the desktop.
• Set the syringe to 20 cc volume.
• Connect the 20mL plastic syringe directly to the stem, as shown in figure 3, to secure the
connection twist the syringe with a gentle 1/2 turn. The pressure inside the syringe is now equal to
atmospheric pressure at the selected volume.
• Open Boyle’s Law file from Physics_Experiments folder
• Click the Collect button and monitor the pressure in the data table. Make sure that the pressure on
the syringe keeps the volume at 20 cc while your are collecting the data.
• When this pressure has stabilized, read the volume on the syringe and click Keep button. A data entry box will appear allowing you to enter the volume of air in the syringe; in this box you
should record the syringe volume in cc (i.e. 20).
• Decrease the volume to 15 cc and take a new pressure measurement. Again let the pressure
stabilise before you click the Keep button.
• Collect the pressure for the volumes of 12 cc, 10 cc, and 7 cc by following the same procedure
outlined in the previous steps.
• Click Stop once you have taken all the readings
• Save this data in D drive or USB drive: under a filename that consists of six characters. The first
three characters should correspond to the first three letters in your last name and the last three
characters should be Boy. Example Rac_Boy for Rachid.
B. Gay-Lussac’s law:
• Plug the temperature probe in Channel 1, and the pressure sensor in Channel 2.
• Connect the white valve stems to one end of the long piece of plastic tubing.
• Connect the other end of the plastic tubing to one of the stems on the rubber stoppers (figure 2).
This rubber stopper should, in turn, be inserted into the Erlenmeyer flask to provide a constant-
volume gas sample.
Note: the 2nd valve on the rubber stopper is shown in a closed position. (Check this?!).
42
• Insert the Erlenmeyer flask in a cold water bath of the beaker (make sure that the beaker is not too
full of water, so that no water splash over).
• Open the GAY-LUSSAC file from the File menu.
• Set the experimental time to 10 minutes.
• Place the water baths on top of the heating plate, and immersed in the water you should have
Erlenmeyer flask and the Temperature Probe. Make sure that the temperature probe is not
touching the walls of the water bath.
• Set the heater at 3/4 of its full scale, and then turn it on.
• Click the Collect button to have the computer collect data for the change in pressure as a function
of temperature for the period of 10 minutes.
• Save this data in drive E or USB drive: under a filename that consists of six characters. The first
three characters should correspond to the first three letters in your last name and the last three
characters should be Gls, Example Rac_Gls for Rachid.
ANALYSIS OF RESULTS:
A. Boyl’s law experiment:
• In a new column of the data table from the saved Boyle’s experiment file have the computer
calculate the product PV for each pressure.(Datanew calculated column)
• Leave the Graph and the Data windows on your screen and close the text window. Call the
laboratory instructor to check your results.
• Plot a second curve using the values of the pressure as the dependent variable and the
corresponding values of 1/V as the independent variable. You can easily graph pressure vs. the
reciprocal of the volume by clicking on the "volume" label on the x-axis of the graph, and from
the list of columns that will appear; select "1/V" then click on the "autoscale button ".
• Using the curve fitting options in the Analyze menu, show how your results and curves verify
Boyle’s law. Explain the shape of the curves.
B. Gay-Lussac’s law:
• From the saved data file for the Gay-Lussac experiment, using the curve fitting option in the
Analyze menu, and show how your results verify the Gay-lussac’s law.
• Explain what the slope of the curve represents.
QUESTIONS:
1- Explain what effect a change in temperature will have on the Boyle’s law experiment.
2- What is the barometric pressure in Ifrane? Would you expect this value to be different than the
barometric pressure in Rabat? Explain your reasoning.
43
EXPERIMENT 7
GAS LAWS (BOYLE’S AND GAY-LUSSAC’S LAW)
NAME: DATE: .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB.
SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points )
Briefly outline the apparatus
General procedures adopted.
PHY 1400 LABORATORY REPORT
44
3. DATA and ANALYSIS:
Attach computer printouts from the Logger Pro Program with the Table window showing PV
column, and the Pressure-versus-Volume graph: (15 points)
Attach computer printouts from the Logger Program with the plot of P-versus-1/V graph with
the corresponding automatic curve fit: (15 points)
Comparison of the graphs with Boyle’s law: (5 points)
Explain the shape of the curves: (10 points)
Attach computer printouts from the LoggerPro Program with the Pressure-versus-Temperature
graph and the corresponding automatic curve fit: (15 points)
Comparison of the graph results with the Gay-lussac’s law: (5 points)
Slope of Pressure-versus-Temperature graph and its physical significance: (10 points)
45
CONCLUSIONS: (10 points)
QUESTIONS: (5 points)
46
EXPERIMENT 8
BUOYANT FORCES
INTRODUCTION:
The purpose of this experiment is to determine buoyant forces on submerged solid objects,
and to investigate the dependence of buoyant forces on volumes and masses of submerged objects
BACKGROUND:
When a solid objects submerged in a fluid (gas or liquid), an upward force is exerted by the
fluid on the object. This force is called the buoyant force (B). The magnitude of the buoyant force
always equals the weight of the fluid displaced by the object (Archimede’s Principle). In other words,
B = ρf Vg
where,
ρf = Density of fluids (mass/unit volume of fluid)
V = Volume of the solid object
g = Gravitational acceleration (9.81 m/sec²)
Let us examine the external forces acting on an object submerged in a fluid (see figure 1).
The object is supported by a string attached to a balance. Assuming the system is in equilibrium,
then:
B = mg - T1
where T1 = Tension in the string (weight of the object when submerged).
If the same object is weighed in air and assuming no buoyant force due to air:
mg = T2
From equation 2 and 3 one can find that,
B = T2 - T1 = (weight of the object in air) - (weight of the object in fluid)
Figure 1: Set-up and Analysis of Buoyant Forces
The apparatus shown in figure 1 will be used for this experiment. The spring balance
provided has a special hook attached to the bottom. Masses to be measured should be attached to this
hook, and their weight should be read from the spring balance scale.
(1)
(Eq. 2)
(Eq. 3)
(Eq. 4)
mg
T2
mg
T1
B
-
-
-
-
Spring balance
Container filled with
liquid
Suspended sphere
47
THE EXPERIMENT:
1- Experimental Apparatus:
The apparatus for this experiment consists of:
Spring balance, masses to be measured, and beaker, Vernier-calliper
2- Experimental Procedure:
A. Measurements for Different Spheres With the Same Volume:
Spheres of different masses but of equal volumes are provided for the purpose of this study.
Prepare a table to record your results as you proceed.
• Measure the dimensions of these spheres and be sure that their volumes are almost the same. Use
a vernier for these measurements.
• Attach one of the spheres to the spring balance.
• Measure the mass of the sphere in air.
• Continue to measure the masses of other spheres in air.
• Submerge one sphere in liquid measure its mass while in the liquid.
• Do the same for other spheres and find their masses while in liquid.
• Use equation # 4 to determine the buoyant force in each case.
• Record your results and include units.
B. Measurements with Different Masses:
Another set of spheres of different volumes and masses are provided for the purpose of this
part of the experiment. Again, prepare another table to record the results of this part and proceed as
follows:
• Use a vernier to measure the dimensions of all masses ( except those that were used in part A).
• Find the volume of each mass.
• Measure the masses of the spheres in air.
• Submerge one sphere in liquid measure its mass while in the liquid.
• Do the same for other spheres and find their masses while in liquid.
• Use equation # 4 to determine the buoyant force in each case.
• Record your results and include units.
• Use graph paper to plot buoyant force versus volume of submerged object for each liquid.
DATA ANALYSIS:
Now with all these data at hand, you should be able to answer the following questions:
• What conclusion could by reach on the basis of the results of part A
• Do you think that the above conclusion would be reached if you use another liquid? Explain.
• Using the results of part B (graph), determine the density of water.
48
EXPERIMENT 8
BUOYANT FORCES
NAME: . DATE: .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB.
SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS:
Briefly outline the apparatus used and the general procedures adopted. (5 points )
PHY 1400 LABORATORY REPORT
49
3. RESULTS AND ANALYSIS
A. Measurements for Different Spheres With the Same Volume:
Data (25 points )
Data Table I:
Object
Measured
Length
(cm)
radius
(cm)
Volume
(cm3)
Mass in
air (g)
Mass in
fluid (g)
Buoyant force
(N)
Calculations Show your work for one of the objects measured (5 points)
50
B. Measurements with Different Masses:
Data (25 points )
Data Table II:
Mass
Measured
Length
(cm)
radius
(cm)
Volume
(cm3)
Mass in
air (g)
Mass in
fluid (g)
Buoyant
force (N)
Calculations Show your work for one of the objects measured (5 points)
GRAPH (15 points)
QUESTIONS (15 points)
51
EXPERIMENT 9
THE FORMATION OF STANDING WAVES --MELDE’S EXPERIMENT
INTRODUCTION:
By sound we mean that phenomenon which is capable of stimulating the sensation of hearing.
Sound always originates in some type of motion. In many instances the source of sound is a standing
wave in some vibrating body, e.g. a drum-head, the vocal cords, a guitar string, or the air column in an
organ pipe. Our goal in this experiment is to learn both about the formation of standing waves in
strings and about the boundary conditions that determine the pitch (frequency) of the sound produced.
THEORY:
Imagine a long string attached to the wall at one end, we grasp the other end, place the string
under some tension T and vibrate this end up and down at some constant frequency f.
Successive crests and troughs are
produced by the motion of the hand and are seen to
move in succession down the string with constant
speed v. Such a wave is called a traveling wave.
The distance between any two successive points in
the wave train which have the same phase is called
the wavelength λ. Careful study shows that the
wavelength λ, frequency f, and wave speed are
related by the wave equation.
v f= λ (Eq1)
Experiments also show that the speed of the wave through the string is independent of the
frequency and amplitude of the wave. It depends only on the characteristics of the medium (the
string) through which the wave moves. This is a general property of many types of wave motion.
Specifically, the speed of the traveling wave in the string is related to the tension in the string T and
the linear density of the string µ (the mass per unit length of the string). The velocity is given by
v T= µ (Eq. 2)
In this experiment, we use an electrically
driven turning fork to generate the wave and we
are interested in the standing waves that are
produced in the string under certain circumstances.
Consider the following situation (see the diagram
to the right). A traveling wave produced by the
vibration of the fork. The wave moves to the right
where it encounters the wall. If the wall was not
present and the string was longer, the wave would
have continued beyond the wall as shown by the
dotted wave. However the wall is present and the
initial traveling wave (solid wave-form) is
reflected back into the string as a second traveling
wave (see second sketch).
The instantaneous shape of the string is found by adding together the displacements that would
be produced by the two waves acting independently.
52
The series of sketches on the right show the
resulting wave form (shape of the string) at six
different times as the incident wave continues to
move to the right and the reflected wave continues
to move to the left. NOTE that there are points on
the string (called nodes, N) where the
instantaneous displacement of the string is also
zero. At intermediate points the wave amplitude
builds up to a positive maximum, dies out and then
builds to a negative maximum. Thus instead of
seeing waves move successively down the string,
one sees the string vibrating in a series of loops.
Each loop is one half wavelength in extent. This
type of wave is called a standing wave or a
stationary wave.
Standing waves will form in the string
only if certain boundary conditions are satisfied.
Specifically, the length of the string must be some
integral number of half-wavelengths for the initial
traveling wave. Since the wave frequency of is
fixed by the fork, this means that we can adjust the
string tension in and therefore the wave speed until
the wavelength satisfies this condition.
Under these circumstances, the string vibrates with the same frequency as the fork, i.e. the
system is said to be in resonance and energy flows from the fork into the vibrating string. The
amplitude of the string builds to quite large magnitudes at resonance.
THE EXPERIMENT:
1- Experimental Apparatus:
Your laboratory station should be equipped with the following items: electrical tuning fork,
string, power supply, weight hanger, slotted weights, meter stick, and electrical balance.
2- Experimental Procedure:
• Attach the string to the fork and pass it over the pulley to the weight hanger.
• Start the fork vibrating and adjust the hanging weight until the string vibrates in a series of
distinct loops.
• Adjust the weight carefully so as to arrive at the approximation of the resonant condition;
Examine the wave motion carefully. Are all the loops of the same size? Is the point where the
string is attached to the fork a nodal point?
• In Table 1 of your laboratory report record the number of vibrating segments of the string, n, the
tension in the string (Newtons), and the wavelength (meters). NOTE that the best value for the
wavelength is just twice the average length of a loop in the vibrating string.
• Repeat the above observations for at least five different values of n.
• Record the frequency of the fork
• Measure the mass of the string and its length, then calculate its linear density, that is mass per unit
length (use the electronic balance to determine the string’s mass).
ANALYSIS OF RESULTS:
• On a graph paper plot the wave velocity-versus-tension.
53
• On the same graph paper plot the wave velocity squared-versus-tension. Watch your coordinates
labels, graph titles, etc.
• What conclusions can be drawn from each of the two graphs?
• Determine the slope of the wave velocity squared-versus-tension graph. Show your work and the
results directly on the graph paper.
• Calculate the linear density of the string from the slope just determined and compare it with the
value you found using the electronic balance. Show all work.
54
EXPERIMENT 9
THE FORMATION OF STANDING WAVES --MELDE’S EXPERIMENT
NAME: . DATE: .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB.
SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS:
Briefly outline the apparatus used and the general procedures adopted. (5 points )
PHY 1400 LABORATORY REPORT
55
3. DATA and ANALYSIS:
TABLE 1: (20 points)
n
T
λ
v
v²
Mass of String:
Linear Density Measurement: (10 points)
Summery of Graphs: (10 points)
Comparison between linear densities of string: (10 points)
CONCLUSION: (10 points)
GRAPH: (30 points)
56
EXPERIMENT 10
ELECTRIC FIELDS AND LINES OF FORCE
INTRODUCTION:
A fixed distribution of electric charge causes an electric force to act on every other electric
charge in the universe. This experiment will serve to examine certain electric fields, and in particular
to map the equipotential lines of an electric field and hence determine the electric lines of force.
THEORY:
The first quantitative investigation of the law of force between electrically charged bodies was
carried out by C. A. Coulomb. His measurements showed that the force of attraction for unlike
charges or repulsion for like charges followed an inverse square law of distance of separation. It was
later shown that for a given distance of separation r the force is proportional to the product of the
individual charges Q and Q’, and is a function of the nature of the medium surrounding the charges.
Expressed in symbols, Coulomb’s law is
F QQ Kr∝ ' 2 (1)
where the factor K, called the dielectric constant, is introduced to take care of the nature of the
medium. The factor K is arbitrarily assigned a value of 1 for empty space. Coulomb’s Law is
restricted to point charges.
In the electrostatic system forces are expressed in dynes, distances in centimeters, and the unit of
charge, called the statcoulomb, is chosen of such magnitude that the proportionality constant in
coulomb’s law is equal to unity. Thus coulomb’s law may be expressed by,
F QQ Kr= ' 2
(2)
An electric field, commonly called field of force, is a region in which forces act on electric
charges if present. If a force F acts on a charge q at a point in the field, the field strength E, by
definition the force per unit charge, is
qFE = (3)
The magnitude of electric field strength is the force per unit charge. Force is a vector quantity having
direction as well as magnitude. The direction of an electric field at any point is the direction of the
force on a positive test charge placed at the point in the field.
Faraday introduced the concept of lines of force to visualize
the strength and direction of an electric field. A line of force is the
path that a free test charge would follow in traversing the electric
field. The path is everywhere tangent to the field direction at each
point. As an illustration, consider the isolated positive charge Q
placed at A in Figure 1. A small positive test charge q at any point
in the field experiences a radial force of repulsion from A. The
lines of force are drawn with arrows to point this direction. When
Q is a negative charge, that is an excess of electrons, these lines
would be directed towards A to indicate an attraction of the
positive test charge q.
The magnitude of the force per unit charge may also be graphically shown by the artifice of lines
of force. By convention, the number of lines of forces drawn through a unit area placed normal to the
field at the point considered, is made numerically equal to the field strength. For example, if the field
Figure 1: E around an isolated positive charge.
57
strength at a point is 5 dynes per statcoulomb, one visualizes 5 lines of force per square centimeter at
that position in the field.
The diagram of Figure 2 shows a plane section near a
pair of equal charges of opposite sign. Each charge exerts a
force on a unit test charge placed in the field. The resultant
force is the vector sum of these forces. Thus, at a point b, f1
is the repulsion force on the unit test charge due to the
positive charge on A, and f2 is the force of attraction to the
negative charge on B. The resultant R is tangent to the line
of force at the point b.
It is evident that a uniform field is represented by a set
of parallel lines of force. A converging set of lines of force
indicates a field of increasing strength; while a field of
decreasing strength would be represented by a diverging set
of these lines.
When charged bodies of different potentials are located in a medium in which some flow of
charge can occur, the field of force will cause these charges to be transported from one body to the
other. To maintain the difference of potential the bodies must then be connected to a source of
electromotive force. The flow lines of the charge follow the paths of the lines of force, that is, they
are also at all points perpendicular to the equipotential surfaces.
THE EXPERIMENT:
1- Experimental Apparatus:
Your lab station should be equipped with the following: Field mapping board and U-shaped
probe, Figure 5. Eight similar resistors connected in series (A to I in Figure 5) and mounted on this
board. Field plates with conductive and corresponding template. Source of potential, and sensitive
galvanometer as a null-point detector.
Figure 5: Experimental Apparatus For Electric Field Mapping Apparatus.
2- Experimental Procedure:
• The power supply should be set to a current of 0.2 A and a voltage of 4 V.
• Prepare the electric field mapping apparatus with the provided field plate securely in place.
• Binding posts marked “Bat.” and Osc.” are located on the upper side of the board. Connect the
DC power supply to the appropriate binding post (point X and Y in Figure 5). When the voltage
Figure 2: Electric Field Near Two
Equal Charges of Opposite Sign.
58
is applied to the terminals, charges flow between them across the field plate following the lines of
force of the electric field established. This same potential difference will be equally divided
between the end terminals of the series of similar resistors.
• Fasten a sheet of graph paper to the upper side of the board. The paper is secured by depressing
the board on either side and slipping the paper under the four rubber bumpers.
• Select the design template (plastic template) containing the field plate configuration you have
chosen. Place the design template on the two metal projections (template guides) above the paper
edge and let the two holes on top of the template slide over the projections. Trace the design
corresponding to the field plate pattern in place on the underside of the mapping board and
remove the template.
• Carefully slide the U-shaped probe onto the mapping board with the ball end facing the underside
of the field mapping board. Connect one lead of the null-point detector (galvanometer) to the U-
shaped probe and one to one of the banana jacks, which are numbered E1 through E7.
• Using the selected banana jack, move the U-shaped probe over the paper to a zero reading of the
galvanometer (Make sure that the galvanometer does not go off scale, that will damage it).
• The circular hole in the top arm of the probe is directly above the contact point that touches the
graphite-coated paper. Record the location of the equipotential point directly on the paper.
• Move the probe to another null-point position and record it.
• Continue this procedure until you have generated a series of these points across the paper. All the
points corresponding to the same equipotential curve should be labeled with the number of the
corresponding resistor (i.e. E1 or E2...etc.).
• Connect the equipotential points with a smooth curve to show the equipotential line of that
banana jack. For example the series of points all of the same potential as C in Figure 5, define an
equipotential line.
• Connect the detector to a new banana jack and plot its equipotential line.
• Repeat until equipotential lines are plotted for all banana jacks E1 through E7.
• Since the potential difference is the same across each similar resistor, the equipotential lines
obtained will be spaced to show an equal potential drop between successive lines.
• With the help of a voltmeter record the potential drop across each series resistors and record in
Table 1 of your laboratory report.
ANALYSIS OF RESULTS:
• The flow lines or lines of force are everywhere perpendicular to the equipotential lines. Draw in,
by dash lines, the lines of force for the electric fields studied.
59
EXPERIMENT 10
ELECTRIC FIELDS AND LINES OF FORCE
NAME: . DATE: .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB.
SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS:
Briefly outline the apparatus used and the general procedures adopted. (5 points )
PHY 1400 LABORATORY REPORT
60
3. RESULTS AND ANALYSIS:
Table 1: Potential Drop Across the Resistors (25 points)
Resistor 1 2 3 4 5 6 7 8
VR
Attach the Graphs: (55 points)
CONCLUSIONS: (10 points)
61
EXPERIMENT 11
GETTING FAMILIAR WITH THE OSCILLOSCOPE
INTRODUCTION:
Modern electronic instruments with their tremendous diversity are no more than sophisticated
combinations of signal generation, signal processing, and signal displaying. In most cases, the
“signal” is an electric current (I). The current passing through a resistor (a barrier in the way of the
current, characterized by the resistance, R) generates a voltage (V) across the resistor, according to:
IRV= (1)
(known as “Ohm’s law). Thus, the signal can be measured as a voltage between the two ends of the
given resistor. The measured signal is characterized by its intensity (in volts, with + or - sign) and its
temporal properties (i.e. how it varies as a function of time). The signal intensity could be measured
by a simple voltmeter but if the signal does vary with time, only slow changes can be followed by this
way. A universal tool to measure both the intensity and temporal behavior of an electric signal is the
oscilloscope.
THE OSCILLOSCOPE
The key component of the oscilloscope is a cathode ray tube shown in Figure 1. Here a beam of
electrons is ejected from the “electron gun” and is directed to the center of the screen is covered with
a luminescent material emitting light where the electron beam strikes it. The light emission lasts a
fraction of second after the impact (an effect known as “afterglow”).
If the electron pass through an electric field before they strike the screen, they can be deflected
(the electric field exerts a force on the electrons). The cathode ray tube uses a set of parallel metal
plates (electrodes) with a voltage (V) applied to them for generating the deflecting electric field. The
force on the electron is proportional to the size of the applied voltage. With this arrangement the
deviation of the electron beam will be proportional to the voltage between the two electrodes plates.
Thus, if the voltage we wish to measure (i.e. V=IR from equation 1) is applied to a set of deflecting
plates, then the distance the actual beam spot moves from the center on the screen is proportional to
the voltage V. Various calibrated distance-voltage (volts/division) options can be show on the
oscilloscope. The oscilloscope is equipped with a vertical pair of plates for deflecting the electron
beam in the horizontal direction, and with a horizontal pair for deflecting in the vertical direction.
Many oscilloscopes are equipped with two channels for measuring the intensity (voltage) of one or
two electric signals.
Figure 1: The Cathode Ray Tube
62
SIGNAL GENERATOR
This instrument generates sinusoidal AC electric signals with a wide range of adjustable
signal frequencies and intensities (Figure 3). The frequency can be adjusted in decade steps (knob 5)
and in a continuous way between decades (knob 7). The output voltage can be adjusted by the knob 2
on the right side.
THE EXPERIMENT
1- Experimental Apparatus:
The apparatus consists of a Tektronix oscilloscope, a function generator, and a power supply.
2- Experimental Procedure:
DC signals analysis:
• Set each channel (CH1 and CH2) in the GND position
(button 3 of Figure 4).
• Switch on the system and set the INTENSITY (Focus,
and readout) knob on the “Display Controls” (button 3 of
Figure 3) to obtain an easily observable light intensity.
• Turn the sensitivity of both channels to 0.5V/div (knob 1
of Figure 4).
• With any sweep time (knob 1 of Figure 5) adjust the
position of the line on the screen into the center. Do this
by using the POSITION control adjust of both the
horizontal and vertical controls (knob 5 of both Figure 4
and Figure 5).
• On the Horizontal Controls press the X-Y button (knob 6
of Figure 5) so that a bright point appears at the center of
the oscilloscope’s display screen. Reduce the
INTENSITY to a convenient level. Try to get sharpest
point using the FOCUS knob of the “Display
Controls”(Figure 3).
• Check that the VARIABLE control knobs on the
“Vertical” controls, and the SWEEP VARIABLE control
(knob 2 of Figure 4 and Figure 5) are in the
counterclockwise end positions. If the bright spot is not
at the center of the screen, adjust its position horizontally.
• Since we are going to be measuring DC voltages, turn the
input mode switches to DC for both CH1 and CH2
(button 3 of Figure 4).
Figrue 3: Display Control of Oscilloscope
Figure 2: The Oscilloscope.
Figure 4: Vertical Controls of the
Oscilloscope
Figure 5: Oscilloscope
Horizontal Control
63
• The oscilloscope is ready now for the first task.
• Plug the output of the DC power supply to the input channel 1 of the oscilloscope.
• Set the output of the DC supply to a 1.5 V.
• Using the oscilloscope, read the value of the DC voltage from the screen. And Record it on your
laboratory report.
• Turn the VARIABLE control knobs on the “Vertical” controls to 0.5 V/Div and read the voltage
of the signal. Record reading on Table I of your laboratory report.
• Turn the VARIABLE control knobs on the “Vertical” controls to 1 V/Div and read the voltage of
the signal. Record reading on Table I of your laboratory report.
• Eliminate the channel 1 input contribution by turning the respective switch to GND (button 3 of
Figure 4). Record your reading in Table I.
• Activate the channel 1 input to DC (button 3 of Figure 4). Change the polarity of the battery
Record your reading in Table I.
• On the Horizontal Controls press the X-Y button (knob 6 of Figure 5) so that a bright point at the
center of the oscilloscope’s display screen will start moving.
• On the Horizontal Controls turn the SEC/DIV knob clockwise and observe what happens to the
display on the screen. Report the observation on your laboratory report.
• Summarize your observations in two or three sentences. Determine from your data which input
channel gives horizontal and which gives vertical displacement of the beam on the oscilloscope.
AC signals analysis:
• Connect the signal generator output
(input 14 of Figure 6) to the
oscilloscope’s input channel 1.
• Adjust the signal generator frequency to
1000 Hz. You do this by setting the
FREQUENCY control knob (knob 7 of
Figure 6) to 1, and the RANGE button
(button 5 of Figure 6) to 1K.
• Select a sinusoidal function by pressing
the sine button (button 6 of Figure 6).
• Since we are going to be measuring AC voltages,
turn the input mode switches to AC for CH1 of the
oscilloscope (button 3 of Figure 4).
• Keep the oscilloscope sensitivity at 0.5 V/div for
both channels. With the TRIGGER MODE at
AUTO (button 6 of Figure 7) and the source at CH1,
turn your display mode to CH1 (button 1 of Figure
7).
• Select the 0 to 20 VP-P button of the frequency
generator (button 12 of Figure 6), and adjust the
output intensity of the generator to get a full wave
(peak to peak) equal to 2V.
• You should now see several moving waves on the
screen. Rotate the TRIGGER LEVEL (knob 9 of
Figure 7) until the waves are stationary on the screen.
• Change the sweep time (knob 1 of Figure 5) to get
two or three full waves on the screen. Record this
sweep time in Table II.
• Record in Table II the length of one full wave in division units, with 0.1 of division accuracy
together with the sweep time used. (You can move the wave to coincide with a convenient
measurement position using the vertical adjustment knob 5 of Figure 4.)
• Now, use the cursors of Figure 8 for measuring the waveform characteristics.
Figure 6: Front Panel of Function Generator.
Figure 7: Oscilloscope’s Trigger
Controls.
64
• Record the VP-P and the period of the waveform in Table II.
• Change the frequency of the signal generator slowly in both directions. Record the frequency
when only one full wave is seen on the screen.
• Summarize your observation in 2 or 3 sentences.
• Assuming that the oscilloscope is accurate, calculate the percentage error in the calibrated
frequency of the signal generator using:
%( )
errorActual f Measured f
Actual f= ×
−100
Figure 8: Oscilloscopes Measurement and Readout Controls
65
EXPERIMENT 11
GETTING FAMILIAR WITH THE OSCILLOSCOPE
NAME: . DATE: .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB.
SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS:
Briefly outline the apparatus used and the general procedures adopted. (5 points )
PHY 1400 LABORATORY REPORT
66
3. RESULTS AND ANALYSIS DC signals analysis:
Table I: (25 points)
Measurement V/Div setting Voltage reading (V)
1 CH1:
2 CH1:
3 CH1:
4 CH1:
5 CH1:
Observation on the Oscilloscope’s screen as your change the SEC/DIV in the clockwise
direction: (5 points)
Interpretation of DC Signal Analysis: (5 points)
AC signals analysis:
TABLE II: (25 points)
CH1 with 1 kHz Direct Reading Reading With Cursor
Voltage Peak to Peak
Sweep Time
Length of Full Wave
One full wave is at frequency: (10 points)
67
Interpretation of AC signal analysis: (10 points)
% error calculation (10 points)
CONCLUSIONS: (10 points)
68
EXPERIMENT 12
OHM’S LAW
INTRODUCTION:
We will study electricity as a flow of electric charge, sometimes making analogies to the flow
of water through a pipe. In order for electric charge to flow a complete loop, called a circuit, must be
established. A simple electrical circuit consists of three elements:
1. a source of electromotive force, such as battery
2. a load with a resistance, such as a lamp, which operates when a current flows through it, and
3. two or more conducting paths of negligible resistance (wires) which can be used to connect the
source and the load in a closed loop. See figure 1.
Figure 1: A Simple Electrical Circuit.
THEORY:
An electrical circuit transfers energy from one point to another, converging it from electrical
energy to heat, light or mechanical energy. Here are some of the terms used to describe electric
circuits.
A source of electromotive force (emf) is some device in the circuit that produces a separation
of (+) and (-) charges and in doing so provides the energy to move the charges around the circuit. A
typical example is a battery that uses chemical energy to produce an emf. The unit of emf is the volt
(V); 1 V = 1 J/C (Joule per coulomb).
The battery is a source of DC (direct current) emf. The charge accumulates
at the ‘poles’ of the battery, indicated by the long (positive charge) and the
short (negative charge) lines. In a DC circuit the current always flows in
one direction, from the positive pole of the battery to the negative pole
through the circuit.
Electric current is the flow of charged particles, usually expressed as the amount of charge
passing a given point per second. Usually these particles are negatively charged electrons. The unit
of current is the coulomb per second, called an ampere (amp, symbolized by A). The amp is a large
unit of current; we will often work in milliamps.
Resistance is the opposition to the flow of current, and is measured
in ohms (Ω), (1Ω = 1V/A). Resistance depends on several factors such as
length, cross-sectional area, temperature and the type of material through
which the charge is flowing. Some electrical devices (called resistors) are
designed to have a large resistance.
As charge flows through a load (any part of the circuit that has a resistance is in general called
a load; most often our loads will be resistors) energy is dissipated from the circuit, usually in the form
of heat or light. The amount of energy dissipated by the load per coulomb of charge is known as the
potential difference across the load. Potential difference has the same unit as emf, namely the volt,
and gives a measure of energy dissipated in the load per coulomb of charge passing through it.
We will sketch circuits using a set of standard figures, a few of which are shown below.
Current
69
In an AC (alternating current) source the current reverses direction
over intervals of time. For example, the wall outlets of your home
provide an AC current which switches direction 100 times each second.
The ammeter and voltmeter are instruments used to measure current and voltage (either an emf
or a potential difference) respectively. It is important that you become proficient with the use of these
two instruments, as you will be using them quite often.
There are two types of basic electric circuit, series and parallel.
A circuit with only one conducting path is a series circuit. It can contain any number of loads
and sources of emf. Figure 2 is a series circuit, shown schematically.
There are no junctions allowing the current to split in a series circuit; all the elements are placed one
after other. All the current must pass through the source and the resistor(s). Consequently, the
current through each resistor is the same.
For “n” resistors in series the current in every part of the circuit is the same, namely,
I I I In= = = =1 2 K (Eq. 1)
and the voltage across the group of “n” resistors is equal to the sum of the voltages across the
individual resistors, namely,
V V V Vn= + + +1 2 L (Eq. 2)
Using Ohm’s law, V = IR, we find that the total resistance of the series group is equal to the sum of
the individual resistance:
R R R Rn= + + +1 2 L (Eq. 3)
A simple parallel circuit is shown in Figure 3. The opposite ends of each resistor have a
common connection to the source. In this circuit the potential difference of each resistor is the same.
Unlike the series circuit in a parallel circuit, there are one or more junctions that allow the current to
split. Therefore, the current through each resistor need not be the same. A branch with high electrical
resistance will have little electrical current passing through it, and a branch with low resistance will
have a high current flowing through it.
For “n” resistors in parallel connection, the voltage across each resistor is the same as that across any
other resistor; this voltage is also the same as that across the entire group:
V V V Vn= = = =1 2 L (Eq. 4)
and the total current is the sum of the separate currents, that is,
Figure 2: Schematic Diagram of
Two Resistors in Series.
A
B
C
Figure 3: A Parallel Circuit Schematic
Diagram.
A B
C
70
I I I I n= + + +1 2 L (Eq.5)
Using Ohm’s law we find that the reciprocal of the effective resistance of the group is equal
to the sum of the reciprocal of the separate resistance:
1 1 1 1
1 2R R R Rn
= + + +L (Eq. 6)
The product of the current and voltage gives the power dissipated in a resistor.
THE EXPERIMENT:
1- Experimental Apparatus:
Your lab station should be equipped with DC batteries, resistors, mutimeters, variable DC power
supply, breadboard, banana cables, flat cables, and lamps.
2. EXPERIMENTAL PROCEDURE:
• Examine the multi-meter. Notice that it has a positive and
negative terminal. When you measure the emf of a source you
must be careful to observe these polarities; the positive terminal
(or probe) should be connected to the positive terminal of the
source. Likewise, the negative probe should be connected to the
negative terminal of the source. The function key should be set to
the desired V range. The polarity is also important when
measuring the potential difference across a resistor. The positive
probe must touch the end of the resistor with the highest potential
(remember the current flows from plus to minus, with the
potential decreasing at each resistor). Figure 4 shows the correct
use of the voltmeter.
• As with the voltmeter, the polarity of the ammeter is also
important. Current has to flow through the ammeter, so the
circuit should be broken and the ammeter inserted into the
circuit. Like the voltmeter, the positive probe goes to the point
of highest potential. See Figure 5.
A. Batteries in Series and in Parallel:
• With the two batteries mounted in their battery holders, measure the emf of one battery, then the
emf of two batteries in series. When connecting batteries in series, connect them with the
terminals as shown in Figure 6a.
Figure 6: Terminal Connections for: a) Batteries in Series, b) Batteries in Parallel.
Figure 4: Emf Measurement
Figure 5: Current
measurement.
71
• Repeat with two batteries in parallel. Batteries connected in parallel are joined with the positive
and negative terminals with common connections, as shown in Figure 6b. Summarize the results
of these measurements on the worksheet in Table 1.
B. Resistors in Series
• Next, construct the circuit of Figure 2, but complete the connections only when ready to take
measurements.
• Open the circuit at point A to insert the ammeter in the circuit. Observe the proper polarity as
discussed above. Measure and record the current going through the resistances in Table II.
• Then connect the voltmeter across the resistor at points A and B. Double check your work,
referring to Figure 2. Before completing the connections have your lab instructor inspect the
circuit. Measure and record the potential difference of the resistor.
• Repeat this measurement for the second resistor by inserting the ammeter in point B and the
voltmeter between points B and C. Record the results in Table II.
• With the two resistors in series measure the voltage drop (potential difference) across the two
resistors (connect the voltmeter between points A and C, i.e. VR1+R2). Record the value in Table
II of your laboratory.
• In the same manner measure and record the current going through both resistors.
C. Resistors in Parallel:
• Connect a single battery to two resistors in parallel as shown in Figure 3.
• Connect the voltmeter across the resistors at points A and B. Measure and record the voltage drop
across each resistor in Table III.
• By placing the ammeter in series with each one of the resistors, measure and record the current in
Table III.
• With the two resistors in parallel record the current delivered by the battery to the resistors.
• When you are finished completely disconnect the batteries and resistors and using the ohmmeter
measure the resistance of each resistor in the order used throughout the experiment and record
your values in Table IV.
Analysis:
• From Table II, add the values of VR1+ VR2 and compare the results with VR1+R2.
• From Table II compare the values of I1 and I2 with the total current leaving the battery.
• From Table III compare the value of the voltage delivered by the battery to the values of VR1 and
VR2.
• From Table III, add the values of IR1+ IR2 and compare the results with IR1+R2.
• Calculate the total resistance for the series connection by using equation 3.
• Calculate the total resistance for the parallel connection by using equation 6.
72
EXPERIMENT 12
OHM’S LAW
NAME: . DATE: .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB.
SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS:
Briefly outline the apparatus used and the general procedures adopted. (5 points )
PHY 1400 LABORATORY REPORT
73
3. RESULTS AND ANALYSIS
TABLE I: (10 points)
No. of EMF (V)
Batteries SERIES PARALLEL
1
2
TABLE II: (20 points)
No. of SERIES PARALLEL
Resistors Potential Difference
Across R1
Current Potential Difference
Across R1
Current
1
2
TABLE III: (20 points)
Potential Difference in Series
Connection
Current in Parallel
Connection
VR1 VR2 VR1+R2 I1 I2 IR1+R2
TABLE IV: Resistors Values as Measured With the Ohmmeter. (10 points)
Measurements with R1 R2
OHMETER
COLOR CODES
Resistors in Series Analysis: (5 points)
VR1+ VR2 =
Comparison between VR1+ VR2 and VR1+R2:
Comparison between I1 and I2 with IR1+R2:
Resistors in Parallel Analysis: (5 points)
I1 + I2 =
Comparison between I1 + I2 and the total current leaving the battery:
Comparison between the value of the VR1and VR2 and the voltage delivered by the battery:
74
Calculations of total resistance for series connection: (10 points)
Calculations of total resistance for parallel connection: (10 points)
75
EXPERIMENT 13
THE SIMPLE LENS
INTRODUCTION
A lens is an optical system formed by two or more refracting surfaces. Examples of
simple lens systems are eyeglasses, magnifying glasses, and telescopes. These simple systems
may comprise either converging or diverging lenses or a combination of both. A lens is said
to be converging (positive) if the rays from an infinitely placed object converge after passing
through the lens. Conversely, in the case of a diverging (negative) lens, the rays diverge after
passing through the lens.
THEORY:
A converging lens is thicker at the center than the periphery, and the incident parallel
rays converge to form a real image on the opposite side of the lens from the object, Figure 1.
A diverging lens is thinner at the center than at the periphery, and the incident parallel rays
diverge to form a virtual image on the same side of the lens as the object, Figure 2.
The principle axis of a lens is a line through the center of the lens, perpendicular to
both faces. The focal point of a lens is that point on the principal axis through which the
incident rays parallel to the principal axis pass ( for a converging lens) or appear to originate (
for a diverging lens) when refracted by the lens.
focal point focal point
Principal
Axis
f (+) f (-)
Figure 1: Converging Lens. Figure 2: Diverging Lens
The lens formula,
1 1 1p q f+ = (1)
gives the relation between the object distance p, the image distance q and the focal length f
(see Figure 3). The lens should be placed with rays from the object incident on the lens from
the left, and the object distance is considered positive. When the image is to the right of the
lens, the image distance is positive; if the image is to the left, the image distance is negative.
A positive value of q indicates a real image, and a negative value of q indicates a virtual
image.
To find the focal length of a thin lens, it is only necessary to measure p and q by some
method. In the special case of Figures 1 and 2, p is very large and 1/p is approximately equal
to zero; therefore, f = q.
76
f (+)
(a) (b)
Figure 3: Object, Image, and Focal Length for Lenses: a) Converging, b) Diverging.
When two thin lenses are placed in contact, the combined focal length f can be
expressed as,
1 1 11 2f f f= + (2)
where f1 and f2 are the focal length of the respective lenses. If one of the lenses is diverging,
the negative value of f must be used for that lens. The magnification m produced by a lens is
given by
m = q/p (3)
The above formulae are valid for all thin lenses. Remember, from your textbook the
image is either larger than or smaller than the object, it is either real or virtual, and it is either
upright or inverted.
THE EXPERIMENT:
1. APPARATUS:
Thin converging and diverging lenses with their lens stands will be used on the
laboratory optical bench in order to find the real image of a lamps. In your laboratory station
you should find the above mentioned equipment in addition to a DC power supply and
electrical cables.
2. PROCEDURE:
2.1 Lens A
1. Call the thinner of the converging lenses lens A. Measure its focal length by arranging the
apparatus to yield a real image of a very distant object on the screen.
2. Mount the illuminated object, lens A, and the screen on the bench so that a real, inverted,
reduced image is formed on the screen. Measure the image and object distances as well as
the image and the object heights. Compute the focal length of lens A using equation 1.
Compare the measured magnification with the prediction of equation 3.
3. Keep the object and screen fixed and move the lens to produce an enlarged image. Repeat
the measurement of step 2.
Image
Object Object
Image
f (+)
p (+)
f (+)
q (+) f (+)
p (+) f (+)
p (+)
f (-)
q
F1 F2 F1 F2
77
2.2 Lens B
1. Call the thicker of the converging lenses lens B. Measure its focal length by arranging the
apparatus to yield a real image of a very distant object on the screen.
2. Mount the illuminated object, lens B, and the screen on the bench so that a real, inverted,
reduced image is formed on the screen. Measure the image and object distances as well as
the image and the object heights. Compute the focal length of lens B using equation 1.
Compare the measured magnification with the prediction of equation 3.
2.3 Lens C
The diverging lens must be treated a little differently since it is not possible to obtain a
real image on a screen using a single diverging lens alone. Call the diverging lens lens C.
Use lenses B (the thicker of the converging lenses) and C together. Mount them in contact
with one another, keeping a distance between them and repeat the procedures (1) and (1).
78
EXPERIMENT 13
THE SIMPLE LENS
NAME: . DATE: .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB.
SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS:
Briefly outline the apparatus used and the general procedures adopted. (5 points )
PHY 1400 LABORATORY REPORT
79
3. RESULTS AND ANALYSIS
Lens A (20 points)
1) f = . cm
2) p = . cm
q = . cm
f = . cm
Object height = . cm
Image height = . cm
Magnification = .
Calculated Mag. = .
Percent difference = .
3) p = . cm
q = . cm
f = . cm
Object height = . cm
Image height = . cm
Magnification = .
Calculated Mag. = .
Percent difference = .
Lens B (15 points)
1) f = . cm
2) p = . cm
q = . cm
f = . cm
Object height = . cm
Image height = . cm
80
Magnification = .
Calculated Mag. = .
Percent difference = .
Lens C (20 points)
1) Combination f = . cm
Lens C f = . cm
2) p = . cm
q = . cm
Combination f = . cm
Lens C f = . cm
Object height = . cm
Image height = . cm
Magnification = .
Calculated Mag. = .
Percent difference = .
4. CONCLUSIONS: (5 points)