LABORATORY MANUAL

FOUNDATION IN SCIENCE (

UNIVERSITI TUNKU ABDUL RAHMANCENTRE FOR FOUNDATION STUDIES

LABORATORY MANUAL

FHSP1014 PHYSICS I

FOUNDATION IN SCIENCE (S)TRIMESTER 1

UNIVERSITI TUNKU ABDUL RAHMANCENTRE FOR FOUNDATION STUDIES

LABORATORY MANUAL

)

UNIVERSITI TUNKU ABDUL RAHMAN CENTRE FOR FOUNDATION STUDIES

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UNIVERSITI TUNKU ABDUL RAHMAN CENTRE FOR FOUNDATION STUDIES

LABORATORY SAFETY RULES

The following rules must be obeyed by all students in the science laboratory of the faculty. Willful or repeated inadvertent noncompliance may result in dismissal or suspension from the laboratories.

I. No entry without permission: i) Outsiders are not allowed to enter the laboratory without permission.

ii) Visitor must request for a lab coat from the laboratory officer before enteringinto the laboratory.

iii) No student is allowed to enter the laboratory unless permission has been given by the laboratory officer or lecturer.

II. At work in the laboratory:

i) No experiment may be attempted without the knowledge and permission of the lecturer or lab officer.

ii) Laboratory coat must be worn at all times in the laboratory.

iii) Students must wear covered shoes in the laboratory. Students wearing open- toed shoes such as slippers or sandals are not allowed to work in the laboratory.

iv) Safety glasses must be worn when necessary.

v) Mobile phones are to be switched off at all times in the laboratory.

vi) Do not smoke, drink, eat, bite nails or pencils, or apply cosmetics in the laboratory.

vii) Do not pipette chemicals using the mouth.

viii) Do not taste any chemicals, including diluted solutions. If any acid or alkali accidentally enters your eyes or mouth, wash immediately with plenty of water. Inform your lecturer or laboratory staff, and seek medical attention if necessary.

ix) Any accident must be reported to the lecturer or lab officer immediately.

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x) Paper should never be used to light up the Bunsen burners.

xi) Used match sticks, filter papers, and other solid waste must never be thrown into the sinks. They must be thrown into the dustbins provided. Lighted match sticks and smoldering materials must be extinguished with tap water before being thrown into the dustbins.

xii) Students must take responsibility for apparatus and equipment under their charge in the laboratory.

xiii) Any glassware breakages, apparatus that are lost and damage to equipment damages or malfunctioning must be reported to the laboratory officer.

III. Before leaving the laboratory:

i) Ensure that all the equipment and work benches used are thoroughly cleaned and dried.

ii) As necessary, wash your hands and arms with soap and water before leaving the laboratory.

iii) All stools must be kept under the benches.

iv) No student is allowed to take away any chemicals, equipment or other property out of the laboratory without permission.

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Introduction

1. Making measurements

Physics is a field of science which is quantitative in nature. In any quantitative study, measurements are made and these measurements should always be regaestimations. The precision of the final result of an experiment cannot be better than the precision of the measurement made during the experiment, so the aim of the experiment is to make the estimations as good as possible. Therefore, repeated at least once to increase its precision and accuracy.

There are many factors that contribute to the accuracy of a measurement. The accuracy in a particular experiment may be due to the observer, or to the instrument used, or to a combination of both.

Errors have a special meaning in science. Errors mistakes because errors cannot be avoided in measurements. Students doing experiments MUST record the uncertainties and errors in their measurement. Students Merrors and uncertainties into account when calculating and presenting their results in laboratory reports.

2. Scrutinize and inscribe the readings

(i) Vernier caliper

Parts of a vernier caliper:

1. Outside jaws2. Inside jaws3. Depth probe4. Main scale5. Main scale6. Vernier (cm)7. Vernier (inch)8. Retainer: used to block the movable part so as to allow the easy

transferring of a measurement

Making measurements

Physics is a field of science which is quantitative in nature. In any quantitative study, measurements are made and these measurements should always be regaestimations. The precision of the final result of an experiment cannot be better than the precision of the measurement made during the experiment, so the aim of the experiment

estimations as good as possible. Therefore, measurementto increase its precision and accuracy.

There are many factors that contribute to the accuracy of a measurement. The accuracy in a particular experiment may be due to the observer, or to the instrument used,

ation of both.

Errors have a special meaning in science. Errors carry a different meaning from errors cannot be avoided in measurements. Students doing experiments

MUST record the uncertainties and errors in their measurement. Students Merrors and uncertainties into account when calculating and presenting their results in

Scrutinize and inscribe the readings

nier caliper:

Outside jaws: used to measure external lengths Inside jaws: used to measure internal lengths Depth probe: used to measure depths Main scale (cm) Main scale (inch)

(cm) (inch) : used to block the movable part so as to allow the easy

transferring of a measurement

3

Physics is a field of science which is quantitative in nature. In any quantitative study, measurements are made and these measurements should always be regarded as estimations. The precision of the final result of an experiment cannot be better than the precision of the measurement made during the experiment, so the aim of the experiment

measurements should be

There are many factors that contribute to the accuracy of a measurement. The accuracy in a particular experiment may be due to the observer, or to the instrument used,

a different meaning from errors cannot be avoided in measurements. Students doing experiments

MUST record the uncertainties and errors in their measurement. Students MUST take errors and uncertainties into account when calculating and presenting their results in

: used to block the movable part so as to allow the easy

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Both the main scale and the vernier scale readings are making measurement. The main scale is the first reading on the main scale immediately to the left of the zero of the vernier scale while the vernier scale reading is the vernier scale which exactly coincides or aligns w

Example:

(ii) Micrometer screw gauge

In order to measure an object, the object is placed between the anvil and spindle (jaws). The thimble is rotated using the ratchet until the object is lighDO NOT OVER TIGHTEN! Note that the be used to secure the object firmlybe damaged or give an inconsistent reading.ratchet are obtained before taking the reading.

Both the main scale and the vernier scale readings are taken into account while making measurement. The main scale is the first reading on the main scale immediately to the left of the zero of the vernier scale while the vernier scale reading is the vernier scale which exactly coincides or aligns with a mark on the main scale.

Micrometer screw gauge

In order to measure an object, the object is placed between the anvil and spindle The thimble is rotated using the ratchet until the object is ligh

DO NOT OVER TIGHTEN! Note that the ratchet (NOT THE THIMBLE) should be used to secure the object firmly between the jaws, otherwise the instrument could be damaged or give an inconsistent reading. It is recommended that

et are obtained before taking the reading.

2.4 cm+ 0.07 cm = 2.47 cm

4

taken into account while making measurement. The main scale is the first reading on the main scale immediately to the left of the zero of the vernier scale while the vernier scale reading is the mark on

ith a mark on the main scale.

In order to measure an object, the object is placed between the anvil and spindle The thimble is rotated using the ratchet until the object is lightly gripped.

ratchet (NOT THE THIMBLE) should between the jaws, otherwise the instrument could

that 3 clicks of the

0.07 cm = 2.47 cm

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Procedure on how to read the scale on below.

3. Data and error analysis

Performing the experiment and collecting data is only the beginning oprocess of completing an experiment in science. Understanding the results of any given experiment is always the central goal of the experiment. Presenting those results in a clear concise manner completes the experiment. This overview of the completeas valid in an instructional laboratory course as in a research environment. You will not have learned any physics if you did not understand the experiment.

Data analysis should not be delayed until all of the data is recorded. Try to do a quick analysis and plot as the data is being collected. This will help to avoid the problem of spending a long time collecting bad data because of a mistake in experimental procedure or an equipment failure.

Data analysis means understanding what your resuthe data, try to think through the physical processes which have occurred. Write your train of thought down. Ultimately, the goal is for you to understand physics and the world a bit better. Your understanding of your results probeing a refinement.

Sometimes your results will not support and may even contradict the physical explanations suggested. Accept the results but with a few suggestions to the reasons for this apparent failure of theexplain what went wrong or what competing effects have come into play.

Procedure on how to read the scale on a micrometer screw gauge is shown in the figure

Data and error analysis

Performing the experiment and collecting data is only the beginning oprocess of completing an experiment in science. Understanding the results of any given experiment is always the central goal of the experiment. Presenting those results in a clear concise manner completes the experiment. This overview of the completeas valid in an instructional laboratory course as in a research environment. You will not have learned any physics if you did not understand the experiment.

Data analysis should not be delayed until all of the data is recorded. Try to do a ick analysis and plot as the data is being collected. This will help to avoid the problem

of spending a long time collecting bad data because of a mistake in experimental procedure or an equipment failure.

Data analysis means understanding what your results mean. When you analyze the data, try to think through the physical processes which have occurred. Write your train of thought down. Ultimately, the goal is for you to understand physics and the world a bit better. Your understanding of your results probably occurs in stages, with each stage

Sometimes your results will not support and may even contradict the physical explanations suggested. Accept the results but with a few suggestions to the reasons for this apparent failure of the physical laws. Do NOT simply blame the equipments. Try to explain what went wrong or what competing effects have come into play.

5

micrometer screw gauge is shown in the figure

Performing the experiment and collecting data is only the beginning of the process of completing an experiment in science. Understanding the results of any given experiment is always the central goal of the experiment. Presenting those results in a clear concise manner completes the experiment. This overview of the complete process is as valid in an instructional laboratory course as in a research environment. You will not

Data analysis should not be delayed until all of the data is recorded. Try to do a ick analysis and plot as the data is being collected. This will help to avoid the problem

of spending a long time collecting bad data because of a mistake in experimental

lts mean. When you analyze the data, try to think through the physical processes which have occurred. Write your train of thought down. Ultimately, the goal is for you to understand physics and the world

bably occurs in stages, with each stage

Sometimes your results will not support and may even contradict the physical explanations suggested. Accept the results but with a few suggestions to the reasons for

physical laws. Do NOT simply blame the equipments. Try to explain what went wrong or what competing effects have come into play.

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The quality of the data determines to a great extent what conclusions can be reached from them. If you are looking for a small effect, say a total change of 1 mm, and the uncertainties in your data is 2 mm, then you really cannot make any solid conclusion. A measurement of experimental results is of little value if nothing is known about the probable size of its error.

The quality of a measurement depends on the precision and accuracy of the measurement. A good measurement must be close to the true value and be reproducible.

(i) Quantifying the uncertainty

All measurements have uncertainties or errors. The uncertainty given in any measurement indicates the type of instrument used for the measurement as well as the possible range of values measured. Basically, for analogue measuring instruments, except for the vernier calipers and micrometer screw gauge, the uncertainty is half of the smallest division of the scale. For digital instruments, the uncertainty is given by the smallest difference in the reading.

(ii) Error propagation rules

The Absolute Error of a quantity Z is given by (Z), always 0.

The Relative Error of a quantity Z is given by ( )ZZ

, always 0.

To determine the error in a quantity Z that is the sum of other quantities, add the absolute errors of those quantities (Rules 2 below). To determine the error in a quantity Z that is the product of other quantities, add the relative errors of those quantities (Rules 3, 4, 5 below).

Relation Error 1. Z = cA ( ) ( )AcZ = (Use only ifA is a single term, i.e. Z = 3x) 2.

Z = ABC ( ) ( ) ( ) ( ) ...+++= CBAZ

3. Z = ABC ( ) ( ) ( ) ( ) Z

CC

BB

AAZ

+

+

+

= ...

4. CABZ = ( ) ( ) ( ) ( ) Z

CC

BB

AAZ

+

+

+

= ...

5. zyx CBAZ =

( ) ( ) ( ) ( ) ZCC

zBBy

AA

xZ

+

+

+

= ...

a, b, c, ..., z represent constants. A, B, C, ..., Z represent measured or calculated quantities (A), (B), (C), , (Z) represent the errors in A, B, C, ..., Z respectively.

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(iii) Percentage error and percentage difference

In several of the laboratory exercises, the true value of the quantity being measured will be considered to be known. In those cases, the accuracy of the experiment will be determined by comparing the experimental result with the known value. Normally this will be done by calculating the percentage error of your measurement compared to the given known value. If E stands for the experimental value, and K stands for the known value, then the percentage error is given by

% 100

=

KKE

error Percentage

In other cases, we will measure a given quantity by two different methods. There will then be two different experimental values, E1 and E2, but the true value may not be known. For such cases, we will calculate the percentage difference between the two experimental values. Note that this tells nothing about the accuracy of the experiment, but will be a measure of the precision. The percentage difference between the two measurements is defined as

% 1002 21

12 +

=

EEEE

difference Percentage

4. Graphical representation and analysis of uncertainties in slopes and intercepts

In the physical sciences, it is helpful to represent data in the form of a graph when interpreting the overall trend of the data. Data analysis graphs are useful to determine the relationships that exist between various quantities, how the data is distributed, and so forth, which may be hard to figure out merely by speculatingbased on the tabulated values alone.

There are a few essential aspects when plotting a graph:

Choice of scale Choose a scale for each of the axes with the main divisions on the graph paper

that are easily subdivided and such that the entire range of values that may be obtained is included.If the values to be plotted are exceptionally large or small, use some multiplying factor that permits the use of a maximum of two or three digits to indicate the value of the main division.

Label the title, the abscissa scale (X-axis) and the ordinate scale (Y-axis) After you have decided which variable is to be plotted on which axis, neatly letter

the name of the quantity being plotted together with the proper units. Abbreviate units in

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standard form, e.g. meters (m). Students should always ensure that the correct units are used in the experimental work.

(i) Plotting and drawing the graph and the best-fit line

In drawing the graph, it is not always possible to make all the points lie on a smooth curve. In such cases, a smooth curve should be drawn through the series of points to follow the general trend and thus represent an average.

Before plotting a linear graph, its important to determine the centroid point of the data set. The centroid is the point which shows the mean of X-values and Y-values. The function of the centroid is to reduce the effect of data scattering.

Centroid, ( )

++++++=

NYYY

NXXX NN ...

,

... 2121y,x

Add the centroid point to linear graph and circle the centroid so as to differentiate it from the other points. Then draw the best straight line which must pass through the centroid. This is called the best-fit line.

(ii) Linear Least Squares Fits

Often measurements are taken by changing one variable (call it x) and measuring how the second variable (call it y) changes as a function of the first variable. In many cases of interest, it is assumed that there exists a linear relationship between the two variables. In mathematical terms one can say that the variables obey an equation of the form

cmxy += (Eq. 1)

where m and c are constants. This also implies that if a graph is made with x as the horizontal axis and y as the vertical axis, it will be a straight line with m equal to the slope (y/x) and c equal to the y intercept (the value of y at x = 0).

The question is how to best verify that the data do indeed obey Equation 1. One way is to make a graph of the data, and then try to draw the best straight line possible through the data points. This will give a qualitative answer to the question; it is possible to give a quantitative answer to the question by the process described below.

The measurements are repeated measurements in the sense that they are to be considered together in the attempt to determine to what extent the data obey Equation 1. It is possible to generalize the idea of minimizing the sum of squares of the deviations. The result of the generalization to two-variable linear data is called a linear least squares fit to the data. It is also sometimes referred to as a linear regression.

The aim of the process is to determine the values of m and c that produce the best straight-line fit to the data. Any choice of the values for m and c will produce a straight

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line, with values y determined by the choice of x. For any such straight line (determined by a given m and c) there will be a deviation between each of the measured ys and the ys from the straight-line fit at the value of the measured xs. The least squares fit is that m and c for which the sum of the squares of these deviations is a minimum. The sum of the squares of the deviations are given by the following equations:

2

11

2

11 1

=

n

i

n

i

n

i

n n

iii

xxn

yxyxnm (Eq. 2)

2

11

2

111

2

1

=

n

i

n

i

n

i

n

ii

n

i

n

i

xxn

xyxxyc (Eq. 3)

Here n is the number of data points, xi and yi are the measured values, and the n

1stands

for the summation from i = 1 to i = n.

We can find the best values for the gradient and the intercept of a line through a set of x-y data using Equations 2 and 3. However, it is not possible to decide how many figures m and c should be quoted to until the uncertainties in m and c, which we will write as m and c respectively, have been calculated.

There are a number of mathematical steps required before we can arrive at explicit equations for m and c. We will not go through the steps here, but simply quote the results:

21

2

11

2

21

=

n

i

n

i

m

xxn

n

(Eq. 4)

21

2

11

2

21

1

2

=

n

i

n

i

n

i

c

xxn

x

(Eq. 5)

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where is the uncertainty in each y-value of the data point. It is usual, when fitting a line to data in which the uncertainty in each point is constant, to make this uncertainty to be the standard deviation of the distribution of the y-value about the fitted line. This is given by

21

1

2)(2

1

= n

ii cmxyn

(Eq. 6)

Example

In an experiment to study the behavior of silicon diodes when cooled, the voltage across a diode was measured as a function of the diode temperature. Table 1 shows the data gathered upon which to applythe linear least square fit method in plotting a straight-line graph.

Table 1: Columns required for fitting a line to data using the method of least squares.

xi (K) yi(V) xiyi (KV) xi2 (K2) 300 0.630 189.00 90000 290 0.653 189.37 84100 280 0.670 187.60 78400 270 0.678 183.06 72900 260 0.695 180.70 67600 250 0.705 176.25 62500 240 0.735 176.40 57600 230 0.748 172.40 52900

xi = 2120 yi = 5.514 xiyi = 1454.42 (xi2)= 566000

Now use Equation 2 to find the gradient of the line

132 VK10616.133600

32.54)2120()566000(8

)514.5)(2120()42.1454(8=

=

=m

and use Equation 3 to find the intercept of the line on the y-axis

V1176.133600

6.37553)2120()566000(8

)42.1454)(2120()514.5(5660002 ==

=c

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Table of Contents:

Practical Topic Page

1

The use of the Vernier Caliper and Micrometer Screw Gauge.

12

2

To investigate vector addition.

13

3

To investigate the free fall object.

15

4 The application of Hookes Law, forces in equilibrium and resolution of vector quantities. 17

5

To investigate and determine the coefficient of static friction.

19

6

To observe and describe the principle of centripetal force and centrifugal effect as used in a centrifuge.

22

7 To study the moment of inertia of a flywheel

24

8

Archimedes Principle on buoyancy of fluids.

27

9

To determine the calorific value of simple food products.

30

10

To investigate the effect of buoyancy via PhET buoyancy simulation.

32

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Practical 1 ________________________________________________________________________

The Use of the Vernier Caliper and the Micrometer Screw Gauge

Objective: To determine the density of oil, copper and PVC.

Apparatus and Materials: 1. Measuring cylinder 2. Copper wire 3. PVC tube 4. Micrometer screw gauge 5. Vernier caliper 6. Oil

Equipment: 1. Electronic balance

Part 1: Determination of the density of oil Procedure: 1. Measure the mass of an empty measuring cylinder. 2. Fill the measuring cylinder with 100 cm oil. 3. Measure the mass of the measuring cylinder filled with oil. 4. Calculate the density of oil.

Part 2: Determination of the density of copper Procedure: 1. Measure the length of a copper wire provided. 2. Using a micrometer screw gauge, measure the diameter of the copper wire at

several places. Determine the average diameter of the copper wire. 3. Measure the mass of the copper wire using an electronic balance. 4. Calculate the volume of the copper wire. 5. Calculate the density of copper.

Part 3: Determination of the density of PVC Procedure: 1. You are given a PVC tube. 2. Measure the external and internal diameter of the PVC tube. 3. Measure the length of the PVC tube. 4. Calculate the volume of the PVC tube. 5. Measure the mass of the PVC tube using an electronic balance. 6. Calculate the density of PVC.

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Practical 2 ________________________________________________________________________

To investigate vector addition

Objective: To verify the parallelogram law of forces.

Apparatus and Materials: 1. Pulley 2. 3 clamp-on pulleys 3. Slotted masses 4. Ruler 5. Force table 6. Protractor

Setup:

Figure 2.1 Theory: Forces are vector quantities as they possess both magnitude and direction. When two or more forces are added together, they issue in a resultant force. The magnitude and direction of the resultant force can be obtained using the parallelogram law as shown in Figure 2.2. If P

r and Q

r are two forces added together and is the angle between them, then the

resultant R obtained is the diagonal of the parallelogram constructed by Pr

and Qr

.

Figure 2.2 Using the cosine rule:

( )+=+ oQPQPQP 180cos2222 rrrrrr ++= cos2222 QPQPR rrrrr From the equations above, if the angle between two forces is known, then the magnitude of the resultant can be determined.

Pr

Qr

QPRrrr

+=

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Procedure:

1. Make sure the force table top is horizontal and balanced. Arrange three pulleys with strings on the force table as shown in Figure 2.3. Two of these will be forces P and Q and the third, or equilibrant, will be force R. The magnitude of the equilibrant will be chosen to balance the forces P and Q, creating a total force of zero.

R

Q

P

x

y

Figure 2.3 Force Table, Top View

2. Use masses (slotted masses plus the mass of each hanger) to create the forces P and Q. Place P and Q with a small angle of about 40o between them (that is, at +20o and 20o), and balance them with a suitable amount of mass at R. The system is balanced when the central ring released without touching the center post. Record the magnitudes for P, Q, and R in Table 1.

3. Repeat step 2 with an angle of 60o, 90, 140 and any 2 angles between them. 4. Using an appropriate scale, draw a parallelogram on a graph paper to represent each

set of forces P, Q, R and the angle . 5. For each set of forces P and Q, the magnitude of the resultant R can be obtained by

three methods. First, directly from Table 1; second from the diagonal of the parallelogram formed by P and Q; and third, using the Cosine Rule.

6. Record the results from all the three methods in Table 2. 7. From the Table 2, compare the results of the three methods and give your comments. 8. Does your result verify the parallelogram law of forces? Comment on your answer. 9. When will P2 + Q2 = P + Q2 ?

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Practical 3 _______________________________________________________________________

To investigate the free fall object.

Objective: To determine the acceleration due to gravity, g by using free fall motion.

Apparatus and Materials: 1. Steel ball 2. Carbon paper 3. Meter rule 4. Retort Stand

Theory:

When a body of mass, m falls from a certain height, h above the ground, it experiences a linear motion. The body will obey the usually equation of motion, that is

2

21

atuty += .(3.1)

Let: y= - h = downward displacement of the body from the falling point to the ground. u = 0 m/s, initial of the ball

t = time taken for the body to reach the ground

We obtain the displacement of the body, y as

y=1

2gt2

Figure 3-1

Carbon paper

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Procedure: 1. The apparatus was set up as shown in the Figure 3.1 2. The height, y of the release ball was adjusted above the point of impact and begun

with a small value of y. 3. The value of y was recorded. 4. Release the ball so that it touches the board below. (Stop the stopwatch when the

ball reach the board). 5. Measure and record the vertical distance y and the time taken. 6. 8 set of reading were taken at different values of y and t. 7. Plot a graph of h against t2. 8. Determine the value of g.

Table 1 No Height, h Time, t (0.01)s t2, s2

h (0.05)cm h (0.0005)m t1 t2 tavg 1. 150.00 2. 155.00 3. 160.00 4. 165.00 5. 170.00 6. 175.00 7. 180.00 8. 185.00

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Practical 4 ________________________________________________________________________

The application of Hookes Law, forces in equilibrium and resolution of vector quantities.

Objectives: To find the force constant of a spring

Apparatus and Materials: 1. Spring 2. Plumb-line 3. Protractor 4. Slotted masses 200g with hanger 5. Thread 6. Retort stand 7. Nail or pin

Setup: 1. Set up the apparatus as shown in Figure 8-1 below. 2. Adjust the spring, so that it stretches horizontally. 3. The angle between the plumb-line and the section AB is . 4. The mass of the load is m, its weight is mg.

Figure 8-1

m=200g

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Theory Let: g = 9.8m/s2 m = mass of the load = angle between the plumb-line and the section AB x = extension of the spring k = force constant of the spring l = stretched length of the spring lo = unstretched length of the spring

When the system is in equilibrium, the forces acting at the point B are in equilibrium

Vertically: mg = T cos . (1)

Horizontally: kx = T sin ... (2)

Therefore: kx = mg tan

kmg

xtan

=

A graph of x against tan will yield a straight line.

The gradient is equal tok

mg.

Procedure: 1. Measure the unstretched length, lo of the spring before setting up the apparatus. 2. Adjust the spring, so that it stretches horizontally. 3. Measure the angle between the plumb-line and the section AB. 4. Measure the new length, l of the spring. 5. Calculate the extension, x of the spring. [where x= l lo] 6. Pull the spring side way to vary the length l to obtain six (6) sets of values of

and x. {Note: before taking the value of the angle , make sure that the spring is horizontal.}

7. Tabulate: x, , tan . 8. Determine the gradient of the graph. 9. Determine the force constant, k of the spring.

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Practical 5

To investigate and determine the

Objectives: To investigate and understand what static friction To determine the coefficient of static friction between two surfaces.

Apparatus and Materials:1. A smooth plank as

a retort stand). 2. Plasticine 3. Wooden blocks 4. A piece of smooth/rough material5. Meter rule

Theory: The magnitude of the static frictional force is the force that is necessary to balancetangential forces along a surface

where N is the magnitude of the normal force and The expression sN gives the maximum static frictional force there can beopposing tangential forces exceed it, the result is motion.force is opposite to the direction of the motion the object would have in the absence of friction.

Setup:

To investigate and determine the coefficient of static friction.

To investigate and understand what static friction is. To determine the coefficient of static friction between two surfaces.

Apparatus and Materials: A smooth plank as an inclined plane (students can hold it up by hand or by using

piece of smooth/rough material

The magnitude of the static frictional force is the force that is necessary to balancealong a surface up to some limit, given by,

Ff sN, here N is the magnitude of the normal force and s is the coefficient of static friction.

gives the maximum static frictional force there can beopposing tangential forces exceed it, the result is motion. The direction of the frictional force is opposite to the direction of the motion the object would have in the absence of

Figure 4.1

19

To determine the coefficient of static friction between two surfaces.

by hand or by using

The magnitude of the static frictional force is the force that is necessary to balance other

is the coefficient of static friction. gives the maximum static frictional force there can be. If the

The direction of the frictional force is opposite to the direction of the motion the object would have in the absence of

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Procedure: 1. Set up the track as shown and hold it up using a retort stand if necessary.

2. Measure the length of the plane, l.

3. Record the masses of the wooden blocks (m1& m2) and the piece of smooth/rough material, m3.

Length of plane, l Mass of wooden block 1, m1 Mass of wooden block 2, m2 Mass of smooth/rough material, m3

4. Place a wooden block with the wide surface against the plane. Starting at small angles, increase the angle until the block first starts to move. Record the height and thus find the corresponding angle using trigonometry.

5. Repeat the measurement twice.

6. Repeat the experiment for the narrow wooden side, the wide side of the wooden block affixed with the smooth/rough piece of material, and then the narrow side of it. Height Angle s

1 2 3 1 2 3 1 2 3 Average Wide wooden

Narrow wooden

Wide smooth/rough

Narrow smooth/rough

7. Place a wooden block on top of a wooden block and repeat the measurements (3 times). Height Angle s

1 2 3 1 2 3 1 2 3 Average 1 wooden block

2 wooden blocks

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Data analysis: 1. Draw the free body diagram of the block and the plane, labeling all the forces acting

on the block. 2. At the angle just below the one at which the block begins to move, the forces are in

equilibrium, and thus the net force is zero. Write two equations (x component & y components or components along the slope and perpendicular to the slope) of equilibrium.

3. Use these equations to find an expression for s. Find the average value of s. 4. What are the dimensions of s? 5. Based on your observations from the experiment, is the value of the coefficient of

friction dependent on the area of contact? 6. Does it depend on the material? 7. Do you observe any difference when two wooden blocks are used instead of one?

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Practical 6

To observe and describe the principle of centripetal force and centrifugal effect as used in a centrifuge.

Objectives: To understand the principle of centripetal force. To observe the workings of a centrifuge. To describe centrifugation.

Apparatus and Materials: 1. Iron (III) hydroxide in water, Fe(OH)3 and/or various substances like oil, mud,

soil in water, blood, etc. 2. Centrifuge tubes 3. Centrifuge

Theory: In a centrifuge, there are only two forces that act upon the particles being rotated in the tube. An analysis of the forces using Newtons second law, which states that the acceleration of the tube is directly proportional to the forces acting on it, but indirectly proportional to the mass of the tube andthe materials within it. The forces acting within this system simply includes the total weight of the tube and the materials within it, and the normal reactionat the point where the tube is attached to the centrifuge. This reaction is often called the centripetal force which holds the tube in place during the machines rotation.

Figure 5.1 The Forces Acting in a Centrifuge

These two forces can be resolved into x and y vectors with the vertical direction taken as y and the horizontal direction as x. With these assumptions, the force of the normal reaction in the y direction is equal and opposite to that of its weight. Since these forces cancel each other out, there is no change in velocity in the y direction while the centrifuge is in motion. The x component of the normal reaction, however, reveals that the tube is accelerating towards the left as in the diagram, or more accurately, towards the center of the rotational motion. This acceleration is called the centripetal acceleration.

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Procedure: 1. Fill 10 ml of a centrifuge tube with the selected substances or a combination of

them. 2. Set the centrifuge machine to rotate at an angular speed of 2000 revolutions per

minute. Let it run for 3 minutes. 3. Observe and sketch a diagram of the materials in the tube. 4. Repeat using different materials provided.

Further questions: 1. What is centripetal force and centrifugal force? 2. How do the forces separate the materials in the solution? 3. Give some examples of applications of centrifugation in daily lives together with

explanations.

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Practical 7 _______________________________________________________________________

To study the moment of inertia of a flywheel

Objective: To determine the moment inertia of a flywheel.

Apparatus and Materials: 1. Flywheel 2. Digital stop watch 3. Slotted masses with hanger 4. Meter rule 5. G clamp 6. Thread 7. A soft board to absorb the impact when the slotted masses hit the ground 8. Vernier caliper

Setup: 1. Clamp the flywheel to the side of the bench. 2. One end of the thread is fixed to the flywheel. The other end is tied to the mass

hanger. 3. Roll the thread round the axle of the flywheel. 4. The distance between the base of the hanger and the floor is, h. 5. When you release the masses, the masses will accelerate downward, and flywheel

will have an angular acceleration.

Figure 7-1

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Theory: Let:

T = tension in the string m = mass of the load a = acceleration of the load = angular acceleration of the flywheel g = gravitational acceleration = 9.81 ms-2 R = radius of the axle I = moment of inertia of the flywheel h = initial distance between load and floor t = time taken for the load to touch the floor = friction torque on the flywheel

Acceleration of load:

2t

ha = ............... (1)

Angular acceleration of wheel: Ra

= (2)

For the load: mg T = ma... (3) T = m(g - a)... (4)

Using equation (1) to find the value of a. Using equation (2) and the calculated value of a to find the value of . Using equation (4) and the calculated value of a to find the value of T.

For the wheel: ITR = ... (5)

IT

IR

=

Graph of against T is a straight line, the gradient is s andIR

s = .

Moment of inertia of the flywheel is: .s

RI =

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Procedure:

1. Measure the initial height of the load. This height is fixed. 2. Put mass onto the hanger. 3. Release the load, and start the stop-watch simultaneously. 4. Take the time for the load to touch the floor. 5. Vary the mass of the load, m. Repeat the above steps, and obtain a total of eight

(8) sets of values of m and t. 6. Tabulate: m, t, a, and T. 7. Plot a graph of against T. 8. From the graph, determine the moment of inertia of the flywheel.

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Practical 8

Archimedes Principle on buoyancy of fluids.

Objective: To determine the density of several substances in fluid and to study Archimedes

Principle on the buoyancy of water.

Apparatus and Materials: 1. One medium-sized measuring cylinder and one large measuring cylinder 2. Various objects: stone, plasticine, small block of wood, metal ball, slotted masses. 3. Spring 4. Retort stand

Apparatus: weighing scale, spring scale.

Setup: Setup the apparatus as shown in Figure 7-1.

Figure 7-1

Theory: The density of an object is the mass of the object per unit volume. Hence, by measuring the increase in mass and the corresponding increase in the volume of water, we can calculate the density of each substance that was lowered into the water.

The Archimedes principle states that the magnitude of the buoyant force exerted upon an object that is partially or completely immersed in a fluid is equal to the weight of the fluid that the object displaces.

For a floating object in part 2, the buoyant force, which is equal to the weight of the liquid displaced, is also equal to the weight of the object.

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By noting the increase in volume in part 3, we can calculate the weight of the water that was displaced. Compare this value to the decrease in the weight of the object as it was lowered into the water. Spring scales work by the principle of Hookes Law where the weight measured is proportional to the extension of the spring of the scale.

kxFspring = , where x is the extension of the spring. Hence, mg = kx.

Procedure: Part 1: (for submerged object)

1. Weigh an empty measuring cylinder. 2. Fill a measuring cylinder with water to about 70% and weigh it and measure its

volume. 3. Add a piece of plasticine to the water until it is completely submerged. Measure

its weight and the total volume. 4. Repeat the above procedure with a piece of stone, slotted masses and metal ball.

Part 2: Repeat part 1 with a block of wood. However because the wood floats in the water, only measure the volume of the water and the weight of the wood. Then calculate the weight of the water displaced by the wood: density of water x volume of water displaced. Compare this reading with the weight of the wood.

Part 3: 1. Weigh a set of slotted masses using a spring scale. 2. Add water to a small measuring cylinder and weigh. Measure the volume of

water. 3. Lower the slotted masses into the measuring cylinder of water so that it is

immersed in the water but does not touch the bottom of the measuring cylinder. Note the increase in volume as well as the reading on the scale.

4. Note: if spring scales are not available, a normal spring is used but the length is measured instead for different values of slotted masses to obtain the spring constant before the weights are lowered into the water.

5. Alternatively, weigh the container with the mass immersed in it. The increase in weight

should be equal to that of the water displaced by it.

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Results: Part 1: Submerged Object

Stone Plasticine Slotted masses

Metal ball

Mass of cylinder, m1 Mass of cylinder with water, m2 Mass of water, m2 m1 Mass of cylinder, water and object, m3

Mass of object, m3 m2 Volume of liquid, V1 Volume of liquid and object, V2 Volume of object, V2 V1 Density of object =

3

12

23 / mkgVVmm

=

Part 2: Floating Object. For wooden block, measure as above but calculate as follows:

1

12

Vmm

water

=

Mass of water displaced )( 12 VVwater = Compare this value with m3 m2

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Practical 9

To determine the calorific value of simple food products.

Objective: To calculate the amount of chemical energy stored in each food products.

Apparatus and materials: 1. Calorimeter made of can and small boiling tube. 2. Water (measured using a small measuring cylinder) 3. Thermometer 4. Candle/Bunsen burner and Lighter or matches 5. Weighing balance 6. Food (marshmallows, biscuit, nut, dry pet food, etc. record the food item you

use)

Setup: Set up the apparatus as shown below.

Theory:

We know that the energy that keeps our brain and body going comes from the food we eat. Our digestive system and the cells in our body break down the food and gradually oxidize the resulting molecules to release energy that our cells can use and store.

Boiling tube

Can

Food to be tested

Cork

Needle

Water

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In this experiment, we shall use a simple method to measure the amount of energy that is chemically stored in different types of food. Youll oxidize the food much more rapidly by burning it in air. You'll use a homemade calorimeter to capture and measure the heat energy released by burning. The basic idea of a calorimeter is to capture the released heat energy with a reservoir of water, which has a high capacity for absorbing heat. The temperature of the water reservoir is measured at the beginning and at the end of the experiment. The increase in the temperature (in C) times the mass of the water (in g) will give us the amount of energy captured by the calorimeter, in calories. We can write this in the form of an equation:

Qwater = mcT where:

Qwater is the heat captured, in calories (cal); m is the mass of the water, in grams (g); c is the specific heat capacity of water, which is 1 cal/gC (1 calorie per gram per

degree Celsius); and T is the change in temperature (the final temperature of the water minus the

initial temperature of the water), in degrees Celsius (C).

Procedure: 1. If the food contains some moisture, warm it up over a light flame to reduce the

moisture before weighing and burning in the following steps: 2. Weigh each of the food items to be tested and record the weight. 3. Fill the boiling tube with a small quantity of distilled water. 4. Measure the initial temperature (Ti) of the water. 5. Impale the food item on the needle. 6. Have your calorimeter pieces close at hand, and ready for use. 7. Place the cork on a non-flammable surface. Light the food item (the nuts may take

awhile to catch fire). 8. When the food catches fire, immediately place the large can around the cork, then

carefully place the boiling tube in place above the flame. 9. Allow the food item to burn itself out. 10. Carefully stir the water and measure the final temperature (Tf). Make sure the

thermometer has reached a steady level before recording the value. 11. When the burnt food item has cooled, carefully remove it from the needle and

weigh the remains. 12. For the subsequent sample, increase the mass of water used if the temperature rise

is too large or reduce it if the temperature rise is too small. 13. Repeat these steps for all of the food items. 14. Analyze your data. Calculate the energy released per individual food item (in

calories and Calories*), and the energy per unit weight of each food item (in calories/gram and Calories/gram). From your individual results, calculate the average value for each food type.

*Calories = kcal

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Practical 10 _______________________________________________________________________

To investigate the effect of buoyancy via PhET buoyancy simulation

Objectives: To understand the meaning of buoyancy. To study the effect of buoyancy to a submerged object in liquid.

Apparatus and Materials: http://phet.colorado.edu/en/simulation/buoyancy

Buoyancy and Density Activity

Directions: Go to the following website to use an interactive simulation to work with buoyancy and density.

http://phet.colorado.edu/en/contributions/view/3350

Procedure: Getting Familiar

1. On the Intro screen, mess with the apparatus, changing the blocks, observing what happens when the mass, volume and densities are held constant.

2. Check and uncheck the boxes under Show Forces to see where they act.

Intro: Give a brief description of what the relationship is between mass, volume and density of each object and how it affects whether the object will sink or float.

Lab Setup 1. Click over to the Buoyancy Playground and begin the lab. 2. There are 5 different fluids to choose from in the lab and five different types of materials.

(Styrofoam, wood, ice, brick and aluminum) 3. Use the table supplied to organize your work.

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Lab Procedure: Part 1 1. In each of the scenarios below, determine first, by predicting, whether the object will sink

or float. Use a mass of 2.5 kg. 2. Test each object once you have predicted and record the results.

Part 1: Write an S for sink or an F for float. Predictions first!! Air Gasoline Olive Oil Water Honey Pred. Act. Pred. Act. Pred. Act. Pred. Act. Pred. Act.

Styrofoam Wood Ice

Brick Aluminum

Lab Procedure: Part 2 1. Determine the volume of the fluid when an object is placed in that fluid. 2. Use a mass of 2.5 kg. 3. Record all values for different sets of combinations in the table below.

Air Gasoline Olive Oil Water Honey Styrofoam Wood Ice

Brick Aluminum

Lab Procedure: Part 3 1. In this part of the lab, determine the amount of buoyant force that is acting on each block

of mass 2.5 kg. 2. Determine how you will find the amount of buoyant force or buoyancy. Perhaps try

using the two scales given in the lab. 3. Record these values in the table below.

Air Gasoline Olive Oil Water Honey Styrofoam Wood Ice

Brick Aluminum

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Conclusions: 1. In part 1 of the lab, what happened when the ice was placed in olive oil?

2. In part 2 of the lab, which of the objects had the greatest density?

3. From part 3, what is the relationship between the buoyant force and the weight of an object when the object:

a. Sinks

b. Floats

4. How is it possible to have two objects of the same mass where one object sinks and the other object floats? Use your observations from the Intro part of the lab to answer this question.

Additional Questions:

http://phet.colorado.edu/en/contributions/view/3408

Directions:

Intro Tab: 1. How can you use a block and the other tools on the Intro tab to determine the density of

the Oil?

2. Determine what forces act on an object when the object is placed in a fluid. How are the forces similar and different when the object sinks, floats immersed in the fluid, and when it is only partially submerged.

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3. Give specific examples that you could use to explain what buoyancy is and how an objects weight can appear to change when in a fluid. Make sure to include situations where the object sinks, floats immersed in the fluid, and when it is only partially submerged.

Playground Tab:

4. Explain how you can use the information about the block and the fluid to determine if the block will sinks, floats immersed in the fluid, and when it is only partially submerged.

5. How can you determine the apparent mass of an object if you know the density of the object and the density of the fluid?

Challenge: Explain how an object that is more dense than water can be kept afloat by placing it on an object that is less dense than water.