lab 1: introduction to · web viewin this unit you will examine two different ways that the...

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LAB 1: INTRODUCTION TO MOTION

Slow and steady wins the race.Aesop's fable: The Hare and the Tortoise

OBJECTIVES

• To discover how to measure motion with a motion detector

• To see how motion looks as a distance (position)-time graph• To see how motion looks as a velocity-time graph• To discover the relationship between position-time

and velocity-time graphs.• To begin to explore acceleration-time graphs.

OVERVIEW

In this unit you will examine two different ways that the motion of an object can be represented graphically. You will use a motion detector to plot distance (position) and velocity-time graphs of the motion of your own body and a cart. The study of motion and its mathematical and graphical representation is known as kinematics.

©1993-94 P. Laws, D. Sokoloff, R. ThorntonSupported by National Science Foundation and U.S. Department of Education (FIPSE)Note: These materials may have been modified locally.

2 Real Time Physics: Active Learning Laboratory V1.40--8/94

©1993-94 P. Laws, D. Sokoloff, R. ThorntonSupported by National Science Foundation and U.S. Department of Education (FIPSE)

Real Time Physics: Lab 1: Introduction to Motion Page 1-3Authors: David Sokoloff, Ronald Thornton & Priscilla Laws V1.40--8/94

INVESTIGATION 1: DISTANCE (POSITION)-TIME GRAPHS OF YOUR MOTION

The purpose of this investigation is to learn how to relate graphs of the distance as a function of time to the motions they represent.You will need the following materials:

• MacMotion software (Motion for MS-DOS computers)

• RealTime Physics Mechanics Experiments folder• Motion detector• Universal Laboratory Interface (ULI) • Number line on floor in meters (optional)

How does the distance-time graph look when you move slowly? Quickly? What happens when you move toward the motion detector? Away? After completing this investigation, you should be able to look at a distance-time graph and describe the motion of an object. You should also be able to look at the motion of an object and sketch a graph representing that motion.Comment: "Distance" is short for "distance from the motion detector." The motion detector is the origin from which distances are measured.

• It detects the closest object directly in front of it (including your arms if you swing them as you

walk).• It will not correctly measure anything closer than

1/2 meter. (When making your graphs don't go closer than 1/2 meter from the motion detector.)

• As you walk (or jump, or run), the graph on the computer screen displays how far away from the detector you are.

Activity 1-1: Making Distance-Time Graphs1. Open the MacMotion program. To start the

program, use the mouse to double click on the MacMotion icon. The graph axes should appear on the screen. (Be sure the ULI is connected to the computer and turned on, and the motion detector is plugged into port #2.)



2. When you are ready to start graphing distance, click once on the Start "button" in the bottom left-hand corner of the screen.

3. If you have a number line on the floor and you want the detector to produce readings that agree, stand at the 2-meter mark on the number line and have someone move the detector until the reading is 2 meters.

4. Make distance-time graphs for different walking speeds and directions, and sketch your graphs on the axes.

a. Start at the 1/2-meter mark and make a distance-time graph, walking away from the detector (origin) slowly and steadily.

b. Make a distance-time graph, walking away from the detector (origin) medium fast and steadily.

c. Make a distance-time graph, walking toward the detector (origin) slowly and steadily.

d. Make a distance-time graph, walking toward the detector (origin) medium fast and steadily.

Question 1-1: Describe the difference between the graph you made by walking away slowly and the one made by walking away more quickly.



Question 1-2: Describe the difference between the graph made by walking toward and the one made walking away from the motion detector.

Comment: It is common to refer to the distance of an object from some origin as the position of the object. Since the motion detector is at the origin of the coordinate system, it is better to refer to the graphs you have made as position-time graphs. From now on you will plot position-time graphs.

Prediction 1-1: Predict the position-time graph produced when a person starts at the 1-meter mark, walks away from the detector slowly and steadily for 5 seconds, stops for 5 seconds, and then walks toward the detector quickly. Draw your prediction on the left axes below using a dashed line. Compare predictions with the rest of your group. See if you can all agree. Draw your group's prediction on the left hand axes below using a solid line. (Do not erase your original prediction.) PREDICTION FINAL RESULT

5. Test your prediction. Open the experiment file L1A1-1 (Away and Back). (Select Open on the File menu, find the RealTime Physics Mechanics Experiments folder, and double click with the mouse pointing to this experiment.) Move in the way described above, and graph your motion. When you are satisfied with your graph,



draw your group's final result on the right axes above.

Question 1-3: Is your prediction the same as the final result? If not, describe how you would move to make a graph that looks like your prediction.

Activity 1-2: Matching a Position GraphBy now you should be pretty good at predicting the shape of a graph of your movements. Can you do things the other way around by reading a position-time graph and figuring out how to move to reproduce it? In this activity you will match a position graph shown on the computer screen.1. Open the experiment file called L1A1-2 (Position

Match). A position graph like that shown below will appear on the screen.

Comment: This graph is stored in the computer as Data B. New data from the motion detector are always stored as Data A, and can therefore be collected without erasing the Position Match graph. Clear any data remaining from previous experiments in Data A by selecting Clear Data A from the Data Menu.

2. Move to match the Position Match graph on the computer screen. You may try a number of times. It helps to work in a team. Get the times right. Get the positions right. Each person should take a turn.



Question 1-4: What was the difference in the way you moved to produce the two differently sloped parts of the graph you just matched?

Activity 1-3: Other Position-Time GraphsIt will be less confusing if you remove the Position Match graph from the screen before doing the exercises below. To do this, select Clear Data B from the Data menu. 1. Sketch your own position-time graph on the axes

which follow with a dashed line. Use straight lines, no curves. Now see how well someone in your group can duplicate this graph on the screen by walking in front of the motion detector.

2. Draw the best attempt by a group member to match your position-time graph on the same axes. Use a solid line.

3. Can you make a curved position-time graph? Try to make each of the graphs shown below.

Graph A Graph B Graph C

4. Describe how you must move to produce a position-time graph with each of the shapes shown.



Graph A answer:

Graph B answer:

Graph C answer:

Question 1-5: What is the general difference between motions which result in a straight line position-time graph and those that result in a curved-line position-time graph?



INVESTIGATION 2: VELOCITY-TIME GRAPHS OF MOTION

You have already plotted your position as a function of time. Another way to represent your motion during an interval of time is with a graph which describes how fast and in what direction you are moving. This is a velocity-time graph. Velocity is the rate of change of position with respect to time. It is a quantity which takes into account your speed (how fast you are moving) and also the direction you are moving. Thus, when you examine the motion of an object moving along a line, its velocity can be positive or negative meaning the velocity is in the positive or negative direction.Graphs of velocity over time are more challenging to create and interpret than those for position. A good way to learn to interpret them is to create and examine velocity-time graphs of your own body motions, as you will do in this investigation. You will need the following materials:


• RealTime Physics Mechanics Experiments folder• Motion detector• Universal Laboratory Interface (ULI) • Number line on floor in meters (optional)

Activity 2-1: Making Velocity Graphs1. Set up to graph velocity. Open the experiment

L1A2-1 (Velocity Graphs ) to set up the Velocity axis to read from -1 to 1 m/sec and the Time axis from 0 to 5 sec, as shown on the next page.

2. Graph your velocity for different walking speeds and directions, and sketch your graphs on the axes. (Just draw smooth patterns; leave out smaller bumps that are mostly due to your steps.)a. Make a velocity graph by walking away from the

detector slowly and steadily. Try again until you get a graph you're satisfied with. You may want to change the velocity scale so that the graph fills more of the screen and is clearer. To do this, double click anywhere on the graph and change the velocity range in the dialog box.



Another way to do this is to click the mouse once with the cursor pointing to the maximum axis reading. Type in the new value and hit return.Then sketch your graph on the axes below.

b. Make a velocity graph, walking away from the detector medium fast and steadily.

c. Make a velocity graph, walking toward the detector slowly and steadily.

d. Make a velocity graph, walking toward the detector medium fast and steadily.



Question 2-1: What is the most important difference between the graph made by slowly walking away from the detector and the one made by walking away more quickly?

Question 2-2: How are the velocity-time graphs different for motion away and motion toward the detector?

Prediction 2-1: Predict a velocity graph for a more complicated motion and check your prediction.Each person draw below, using a dashed line your prediction of the velocity graph produced if you:

• walk away from the detector slowly and steadily for about 5 seconds

• stand still for about 5 seconds• walk toward the detector steadily about twice as

fast as beforeCompare your predictions and see if you can all agree. Use a solid line to draw in your group prediction.

PREDICTION

3. Test your prediction. (Be sure to adjust the time scale to 15 seconds. As before. this can be done by clicking the mouse once on the 5 to highlight it,



typing in a 15 and then hitting the return key. ) Repeat your motion until you think it matches the description. Draw the best graph on the axes below. Be sure the 5-second stop shows clearly.

FINAL RESULT

Comment: Velocity implies both speed and direction. How fast you move is your speed, the rate of change of position with respect to time. As you have seen, for motion along a line (e.g., the positive x axis) the sign (+ or -) of the velocity indicates the direction. If you move away from the detector (origin), your velocity is positive, and if you move toward the detector, your velocity is negative.The faster you move away from the origin, the larger positive number your velocity is. The faster you move toward the origin, the "larger" negative number your velocity is. That is -4 m/s is twice as fast as -2 m/s, and both motions are toward the origin.These two ideas of speed and direction can be combined and represented by vectors. A velocity vector is represented by an arrow pointing in the direction of motion. The length of the arrow is drawn proportional to the speed; the longer the arrow, the larger the speed. If you are moving toward the right, your velocity vector can be represented by the arrow shown below.

If you were moving twice as fast toward the right, the arrow representing your velocity vector would look like



while moving twice as fast toward the left would be



represented by the following arrow

What is the relationship between a one-dimensional velocity vector and the sign of velocity? This depends on the way you choose to set the positive x axis.

In both diagrams above, the top vectors represent velocity toward the right. In diagram 1, the x axis has been drawn so that the positive x direction is toward the right, as it is usually drawn. Thus the top arrow represents positive velocity. However, in diagram 2, the positive x direction is toward the left. Thus the top arrow represents negative velocity. Likewise, in both diagrams the bottom arrows represent velocity toward the left. In diagram 1 this is negative velocity, and in diagram 2 it is positive velocity.

Question 2-3: Sketch below velocity vectors representing the three parts of the motion described in Prediction 2-1.

Walking slowly away from the detector:

Standing still:

Walking rapidly toward the detector:

Activity 2-2 Matching a Velocity GraphIn this activity, you will try to move to match a velocity graph shown on the computer screen. This is often much harder than matching a position graph as you did in the previous investigation. Most people find it quite a challenge at first to move so as to match a velocity graph. In fact, some velocity graphs that can be invented cannot be matched! 1. Display the velocity graph on the screen. Pull down

the File Menu and select Open. Find the RealTime



Physics Mechanics Experiments folder, and then double click on



L1A2-2 (Velocity Match). The velocity graph shown below will appear on the screen.

2. Move so as to imitate this graph. You may try a number of times. Work as a team and plan your movements. Get the times right. Get the velocities right. Each person should take a turn. Draw in your group's best match on the axes above.

Question 2-4: Describe how you moved to match each part of the graph.

Question 2-5: Is it possible for an object to move so that it produces an absolutely vertical line on a velocity time graph? Explain.

Question 2-6: Did you run into the motion detector on your return trip? If so, why did this happen? How did you solve the problem? Does a velocity graph tell you where to start? Explain.

If you have more time, try the Extensions for Activity 2-2, at the end of this lab.



INVESTIGATION 3: RELATING POSITION AND VELOCITY GRAPHS

You have looked at position and velocity-time graphs separately. Since position-time and velocity-time graphs are different ways to represent the same motion, it ought to be possible to figure out the velocity at which someone is moving by examining her/his position-time graph. Conversely, you ought to be able to figure out how far someone has traveled (change in position) from a velocity-time graph.To explore how position-time and velocity-time graphs are related, you will need the following materials:


• RealTime Physics Mechanics Experiments folder• Motion detector• Universal Laboratory Interface (ULI)• Number line on floor in meters (optional)

Activity 3-1 Predicting Velocity Graphs from Position Graphs1. Set up to graph Position and Velocity. Open the

experiment L1A3-1 (Velocity from Position) to set up the top graph to display Position from 0 to 4 m for a time of 5 sec, and the bottom graph to display Velocity from -1 to 1 m/sec for 5 sec. Clear any previous graphs.

Prediction 3-1: Predict a velocity graph from a position graph. Carefully study the position-time graph shown below and predict the velocity-time graph that would result from the motion. Using a dashed line, sketch your prediction of the corresponding velocity-time graph on the velocity axes.



2. Test your prediction. After each person has sketched a prediction, Start, and do your group's best to make a position graph like the one shown. Walk as smoothly as possible.When you have made a good duplicate of the position graph, sketch your actual graph over the existing position-time graph.Use a solid line to draw the actual velocity graph on the same graph with your prediction. (Do not erase your prediction).

Question 3-1: How would the position graph be different if you moved faster? Slower?

Question 3-2: How would the velocity graph be different if you moved faster? Slower?

Activity 3-2: Calculating Average VelocityIn this activity, you will find an average velocity from your velocity graph in Activity 3-1 and then from your position graph. 1. Find your average velocity from your velocity graph

in Activity 3-1. Select Analyze Data A in the Analyze menu, read a number of values (say ten) from the portion of your velocity graph where your velocity is relatively constant, and use them to calculate the average (mean) velocity. Write the 10 values in the table below.

Average value of the velocity: ________m/s



Comment: Average velocity during a particular time interval can also be calculated as the change in position divided by the change in time. (The change in position is often called the displacement. ) By definition, this is also the slope of the position-time graph for that time period. As you have observed, the faster you move, the more inclined is your position-time graph. The slope of a position-time graph is a quantitative measure of this incline, and therefore it tells you the velocity of the object.2. Calculate your average velocity from the slope of

your position graph in Activity 3-1. Use Analyze Data A to read the position and time coordinates for two typical points while you were moving. (For a more accurate answer, use two points as far apart as possible but still typical of the motion, and within the time interval over which you took velocity readings in (1).)

Position (m) Time (sec)Point 1Point 2

Calculate the change in position (displacement) between points 1 and 2. Also calculate the corresponding change in time (time interval). Divide the change in position by the change in time to calculate the average velocity. Show your calculations below.

Change in position (m)Time interval (sec)Average velocity (m/s)

Question 3-3: Is the average velocity positive or negative? Is this what you expected?

Question 3-4: Does the average velocity you just calculated from the position graph agree with the average velocity you found from the velocity graph? Do



you expect them to agree? How would you account for any differences?

If you have additional time, try the Extensions for Activity 3-2 at the end of this lab, and use MacMotion to find the average velocity from your graphs. If you are planning to come back to this later, be sure to save your graphs now. (Select Save Experiment As . . . from the File menu, type in a name for the file that you will recognize later and click on Save.)

Activity 3-3 Predicting Position Graphs from Velocity GraphsPrediction 3-2: Carefully study the velocity graph shown below. Using a dashed line, sketch your prediction of the corresponding position graph on the bottom set of axes. (Assume that you started at the 1-meter mark.)

1. Test your prediction. First shut off Analyze by pulling down the Analyze menu until the mouse



points to Analyze Data A. Then reset the Time axis to 0 to 10 sec before you start.

2. After each person has sketched a prediction, do your group's best to duplicate the top (velocity-time) graph by walking. Be sure to graph velocity first. When you have made a good duplicate of the velocity-time graph, draw your actual result over the existing velocity-time graph.

3. Use a solid line to draw the actual position-time graph on the same axes with your prediction. (Do not erase your prediction.)

Question 3-5: How can you tell from a velocity-time graph that the moving object has changed direction?

Question 3-6: What is the velocity at the moment the direction changes?

Question 3-7: Is it possible to actually move your body (or an object) to make vertical lines on a position-time graph? Why or why not? What would the velocity be for a vertical section of a position-time graph?

Question 3-8: How can you tell from a position-time graph that your motion is steady (motion at a constant velocity)?

Question 3-9: How can you tell from a velocity-time graph that your motion is steady (constant velocity)?



If you have more time, do the Extensions for Activity 3-2 at the end of this lab to see other ways of using MacMotion to find the average velocity from a position-time graph.



INVESTIGATION 4: INTRODUCTION TO ACCELERATION

There is a third quantity besides position and velocity which is used to describe the motion of an object--acceleration. Acceleration is defined as the rate of change of velocity with respect to time. In this investigation you will begin to examine the acceleration of objects. Because of the jerky nature of the motion of your body, the acceleration graphs are very complex. It will be easier to examine the motion of a cart.In this investigation you will only examine the cart moving with a constant (steady) velocity. Later, in Lab 2 you will examine the acceleration of more complex motions of the cart. You will need the following:


• RealTime Physics Mechanics Experiments folder• Motion detector• Universal Laboratory Interface (ULI) • Cart or toy car with very little friction.• Smooth ramp or other level surface 2-3 meters

long Activity 4-1: Motion of a Cart at a Constant VelocityTo graph the motion of a cart at a constant velocity you can hold the cart with your hand and push it along a smooth level surface. 1. Set up the motion detector at the end of the ramp.

If the cart has a friction pad, move it out of contact with the ramp so that the cart can move freely.

2. Set up the position and velocity axes shown below by opening the experiment L1A4-1 (Constant Velocity).

Prediction 4-1: Based on your observations of the motions of your body, how should the position and velocity graphs look if you move the cart at a constant velocity away from the motion detector starting at the



0.5 meter mark? Sketch your predictions with dashed lines on the axes which follow.



PREDICTION AND FINAL RESULTS

3. Test your prediction. Single click on the velocity graph to plot velocity first. Be sure that the cart is never closer than 0.5 meter from the motion detector. Start graphing. Try several times until you get a fairly constant velocity. Sketch your results with solid lines on the axes.

Question 4-1: Did your position-time and velocity-time graphs agree with your predictions? What characterizes constant velocity motion on a position-time graph?

Question 4-2: What characterizes constant velocity motion on a velocity-time graph?

Activity 4-2: Acceleration of a Cart Moving at a Constant Velocity

Prediction 4-2: Based on the definition of acceleration, sketch with a dashed line on the axes



which follow your prediction of the acceleration of the cart for the motion you just observed at a constant velocity away from the motion detector.

PREDICTION AND FINAL RESULTS

4. Display the real acceleration graph of the cart in place of the position graph by holding the mouse button down with the cursor on the Position label on your graph and selecting Acceleration. Sketch the acceleration graph using a solid line on the axes above.

Comment: To find the average acceleration of the cart during some time interval (the average rate of change of its velocity with respect to time), you must measure its velocity at the beginning and end of the interval, calculate the difference between the final value and the initial value and divide by the time interval.Question 4-3: Does the acceleration-time graph you observed agree with this method of calculating acceleration? Explain. Does it agree with your prediction?

Question 4-4: The diagram below shows the positions of the cart at equal time intervals. (This is like overlaying



snapshots of the cart at equal time intervals. The motion detector also looks at the cart's position at equal intervals.) At each indicated time, sketch a vector above the cart which might represent the velocity of the cart at that time while it is moving at a constant velocity away from the motion detector. Comment: To find the average acceleration vector from two velocity vectors, you must first find the vector representing the change in velocity by subtracting the initial velocity vector from the final one. Then you divide this vector by the time interval.

Question 4-5: Show below how you would find the vector representing the change in velocity between the times 1 sec and 2 sec in the diagram in Question 4-4. (Hint: the vector difference is the same as the sum of one vector and the negative of the other vector.) From this vector, what value would you calculate for the acceleration? Explain. Is this value in agreement with the acceleration graph on the previous page?



EXTENSIONS FOR LABORATORY 1: INTRODUCTION TO MOTION

Extensions for Activity 2-2: More Velocity GraphsPrediction 1: Can you tell from a velocity-time graph where you were when you started walking and where you were when you stopped walking? Explain.

Set up the motion detector and test your prediction. Make a graph walking away from or toward the motion detector. Move the graph to Data B. Then, for comparison, make a second graph moving in exactly the same manner, but this time start at a different distance from the detector. Sketch or print the graphs. Compare them. Question 1: If someone showed you these graphs, could you tell from the graphs where the person was when s/he started moving? Explain.

Prediction 2: You are driving down the highway, and another car moving in the same direction passes you. At the moment that the car passes you, which motion quantity is the same for both cars--position, velocity or both?

Devise a method to test your prediction. Set up the motion detector to look at two people walking in opposite directions next to one another at the moment one passes the other. (Hint: remember that the motion detector usually detects the object which is closest to it.) Graph the motions. Sketch or print your graph. Compare the results to your prediction.

Question 2: What is your conclusion? Which quantities are the same when one object passes another--their velocities, positions or both?



Extensions for Activity 3-2: Using Statistics . . . and Fit . . . to Find the Average Velocity In Activity 3-2, you found the value of the average velocity for a steady motion in two ways: from the average of a number of values on a velocity-time graph and from the slope of the position-time graph. The Statistics . . . feature in MacMotion allows you to find the average (mean) value directly from the velocity-time graph. The Fit . . . feature allows you to find the best line which fits your position-time graph from Activity 3-1. The equation of this line includes a value for the slope.1. Using Statistics . . . You must first select the

portion of the velocity-time graph for which you want to find the mean value. Select Analyze Data A from the Analyze menu. To highlight the region of the velocity-time graph where you were walking, click once on the graph to select it, and then position the cursor line at the beginning of the desired region. Press and hold down the mouse button, and slide the mouse until the cursor line is at the end of the desired region. Release the mouse button. The region should remain darkened.Next select Statistics . . ., and read the mean value of velocity from the table.

Question 1: Compare this value to the one you found from ten measurements in Activity 3-2. Which method do you think is more accurate? Why?

2. Using Fit . . . You must first select the portion of the position-time graph which you want to fit. Select Analyze Data A from the Analyze menu. To highlight the region of the position-time graph where you were walking, click once on the graph to select it, and then position the cursor line at the beginning of the desired region. Press and hold down the mouse button, and slide the mouse until the cursor line is at the end of the desired region. Release the mouse button. The region should remain darkened.



Next, select Fit . . . from the Analyze menu. Select a linear fit, y = bo + b1*x, and then click on Try Fit.Record the equation of the fit line below, and compare the value of the slope (b1) to the velocity you found in Activity 3-2.

Question 2: What is the meaning of bo?

Question 3: How do the two values of velocity which you found here agree with each other? Is this what you expected?



TEACHERS' NOTES FOR LABORATORY 1: INTRODUCTION TO MOTION

Equipment and Materials• MacMotion software (Motion for MS-DOS computers)• RealTime Physics Mechanics Experiments folder• Motion detector• Universal Laboratory Interface (ULI) • Cart or toy car with very little friction• Smooth ramp or other level surface 2-3 meters long• Number line on floor in meters (optional)

The motion detector is a sonar device, sending out pulses of ultra-sound with a frequency range around 50,000 Hz. (The rate of emission of these pulses is adjustable from 10 to 50 per second. 20 is the default value, which is automatically selected when the program is first run.) After a pulse is emitted, the motion detector converts from a transmitter to a receiver, and listens for echoes. By timing the delay from sending a pulse to receiving an echo, and using the speed of sound in air, the software determines the distance from the detector to the object which reflected the pulse. The software then plots these distances as a function of time. Velocities and accelerations are calculated in real time using a polynomial fit to the distance data.Student body motions have been shown to be very effective in teaching kinematics concepts. Four precautions are necessary to assure reasonable results:1. The motion detector will not correctly measure objects

closer than 0.5 meter from it. Be sure that students never get closer than 0.5 m from the motion detector. It should be able to detect objects out to at least 4 meters.

2. The motion detector sends out ultrasonic waves in a cone of about 15°. It will see the closest object to it within this cone. Extraneous objects should be cleared from students' paths. Be sure to leave lots of room! If the motion detector is consistently seeing something at a fixed distance from it, read this distance off the graph (or using Analyze) and check for objects at that distance from the motion detector. Occasionally the motion detector will even see small cracks in the table or floor. Tilting it a bit upward usually solves this problem.



3. The motion detector will detect small movements of arms, bends of the waist, etc. Best results will be obtained if the motion detector is high enough to be aimed at the chest rather than the legs.

4. Ultrasonic waves are absorbed by bulky materials like Fiberglas and wool. Therefore, the motion detector may not properly see students wearing bulky sweaters. The result is that the maximum distance will be recorded. The best idea is to have the student remove the sweater, if possible. Holding a card or book against the body in front of the motion detector will generally work, but the card (or book) must be held steady while walking, not carelessly moved or waved.

One last consideration. At a data rate of 20 per second, a data point is measured every 0.05 seconds. While some averaging is used in calculating velocities and accelerations, the graphs display a real-world look at body motions. These generally are not smooth--like textbook graphs--unless careful efforts are made to move in a smooth, non-jerky fashion. Smooth, short, shuffling steps will give the most uniform, easiest to interpret graphs. Students are generally able to decide which features of a graph are important. If Sampling and averaging rates should be chosen appropriately for the moving object, if you choose to change them from the values assigned in the experiment files. If motion is looked at over too short a time, the small motions made by clothes, for example, can cause substantial bumps on velocity and acceleration graphs of moving students. If motion is looked at over too long a time, the measurements will not appear responsive to student movements.It is important to have very smooth ramps and low friction carts. Every little change in the motion of the cart caused by small cracks or scratches on the ramp will be seen on the acceleration graphs. PASCO tracks and low friction carts work well. Tables with Formica tops will also work well. For more information, see Equipment and Materials in the Teachers' Notes for Lab 2, Changing Motion. Sample GraphsFigure 1 is a typical distance (position) graph showing someone walking away from the motion detector at a constant, slow velocity, as in Activity 1-1, 4 (a). If you get spikes on your position graphs, it is likely that the motion detector is not aimed correctly, and is intermittently



missing your body. Be sure that you are walking in a line straight away from the motion detector. If the position graph levels out at a certain distance and continues as a horizontal line even though you are still moving away, this indicates that some other object is in the way between you and the motion detector. Check the distance where it levels out using Analyze Data A, and look for any objects which might be in the way.

Figure 2 is a typical velocity graph showing someone walking away from the motion detector at a constant, slow velocity, as in Activity 2-1, 2 (a). Note that the individual steps can be seen as bumps on the velocity-time graph. These can be minimized by taking care not to swing your arms or jerk your body as you walk. Small shuffling steps are best.Figure 3 shows position and velocity graphs for a cart moving at a constant velocity away from the motion detector, as in Activity 4-1. Figure 4 shows the acceleration and velocity graphs for the same motion of the cart, as in Activity 4-2.



If your velocity and acceleration graphs are much bumpier than these, try to move the cart with a steadier velocity.


lab 1: introduction to · web viewin this unit you will examine two different ways that the...

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