lab 3: force and · web viewpage 3-18real time physics: active learning laboratoryv1.40--8/94...

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LAB 3: FORCE AND MOTION

A vulgar Mechanik can practice what he has been taught or seen done, but if he is in an error he knows not how to find it out and correct it, and if you put him out of his road, he is at a stand; whereas he that is able to reason nimbly and judiciously about figure, force and motion, is never at rest til he gets over every rub.

Isaac Newton (1694)

OBJECTIVES

• To develop the concept of force in terms of how it is measured

• To learn how to use a force probe to measure force• To understand the relationship between forces

applied to an object and its motions• To find a mathematical relationship between the

force applied to an object and its acceleration

OVERVIEW

In the previous labs, you have used a motion detector to display position-time, velocity-time and acceleration-time graphs of the motion of different objects. You were not concerned about how you got the objects to move, i.e. what forces (pushes or pulls) acted on the objects. From your experiences, you know that force and motion are related in some way. To start your bicycle moving, you must apply a force to the pedal. To start up your car, you must step on the gas pedal to get

©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

the engine to apply a force to the road through the tires. But, exactly how is force related to the quantities you used in the previous unit to describe motion--position, velocity and acceleration? In this unit you will pay attention to forces and how they affect motion. You will first develop an operational idea of a force as a push or a pull. You will learn how to measure forces. Then you will apply forces to a cart, and observe the nature of its resulting motion graphically with a motion detector.

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

Real Time Physics: Lab 3: Force and Motion-3

Authors: David Sokoloff, Ronald Thornton & Priscilla Laws V1.40--8/94INVESTIGATION 1: MEASURING FORCES

In this investigation you will explore the concept of a constant force and the combination of forces in one dimension. You can use these concepts to learn how to measure forces with a force probe. You will need the following materials:

• MacMotion software (Motion for MS-DOS computers)

• RealTime Physics Mechanics Experiments folder• Force probe• Universal Laboratory Interface (ULI) • Five identical rubber bands• Meter stick• Spring scale with a maximum reading of 5 or 10

N

Activity 1-1: How Large is a Pull?If you pull on a rubber band attached at one end, you know it will stretch. The more you pull, the more it stretches. Try it.



1. Attach one end of the rubber band to something on the table that can't move. Also attach the meter stick to the table. Now stretch the rubber band so it is several centimeters longer than its relaxed length. Does it always seem to exert the same pull on you each time it is stretched to the same length? (Most people agree that this is obvious.)

2. Write down the length you have chosen in the space below. This will be your standard length for future measurements.

Standard length of rubber band = ____ cm3. Attach the ends of two identical rubber

bands in the same way as before, and stretch them both to the standard length.

Question 1-1: How does the combined force of two rubber bands compare to what you felt when only one rubber band was used?

4. Repeat this comparison of how strong the forces feel with three, four and five rubber bands stretched in the same way to the same standard length.


Real Time Physics: Lab 3: Force and MotionPage 3-5

Authors: David Sokoloff, Ronald Thornton & Priscilla Laws V1.40--8/94Question 1-2: Suppose you stretched a rubber band by pulling on it to your standard length. Now you want to create a force six times as large. How could you assure that you are being pulled with such a force?

Question 1-3: Suppose you applied a force with a stretched rubber band one day, and several days later you wanted to feel the same force or apply it to something. How could you assure that the forces were the same? Explain.

Question 1-4: Do rubber bands provide a convenient way of accurately reproducing forces of many different sizes? Explain.

You have seen that pulling more rubber bands to the same length requires a larger pull. In order to be more precise about the pulls and pushes you are applying, you need a device to measure forces accurately. The force probe is designed to do this.

Activity 1-2: Measuring Forces with a Force Probe In this activity you will explore the capability of the force probe as a force measuring device.1. Set up the force probe by plugging it into port 1 of

the ULI. Turn on the ULI, and open the MacMotion software. When the axes appear on the screen, display force by opening the experiment L3A1-2a (Measuring Force).Check that the separation between the magnet and the sensor is about 0.8 cm. If it is too large or too small, adjust it.

Comment: Since forces are detected by the computer system as changes in an electronic signal, it is important to have the computer "read" the signal when the force probe has no force pushing or pulling on it.



This process is called "zeroing". Zeroing is accomplished by clicking on the Zero button in the lower right-hand corner of the screen while there is nothing pulling or pushing on the force probe hook.Also, since the electronic signal from the force probe can change slightly from time to time as the temperature changes, it is always a good idea to Zero the force probe right before taking any measurements.2. Zero the force probe with nothing pulling on it.3. Attach one end of a rubber band to something which

can't move, as before, and the other end to the force probe hook. Pull horizontally on the rubber band with the force probe until the band is stretched to the same standard length used in Activity 1-1, and Start graphing while holding the rubber band steady for the whole graph.Record a typical force probe reading:(Use Analyze Data A on the Analyze menu to get an accurate reading of the force.)

4. Although you could continue to take data with multiple rubber bands in the same way you did with just one, the easiest way to take these data is to load the experiment L3A1-2b (Rubber Bands). This experiment sets the software in "Event Mode" and allows you to plot the measured force against the number of rubber bands. After loading, Zero the force probe and then press Start. A Keep button will appear and a point representing the force probe reading will be displayed on the graph above 0 rubber bands. Press Keep to record this value on the graph. The point will then be displayed above 1 rubber band. Pull one rubber band with the force probe to your standard length, and again press Keep to record the value on the graph. Repeat with 2, 3, 4 and then 5 rubber bands stretched to the same standard length, pressing Keep each time, and then press Stop when you are done.

5. Record the force probe reading for each number of rubber bands in the table below (you may use



Authors: David Sokoloff, Ronald Thornton & Priscilla Laws V1.40--8/94Analyze or look at the Data A Table window to see the values).

Comment: We are interested in the nature of the mathematical relationship between the reading of the force probe and force (in rubber band units). This can be determined from the graph by drawing a smooth curve which fits the plotted data points. Some definitions of possible mathematical relationships are shown below.

In these examples, y might be the force probe reading and x the number of rubber bands.These graphs show the differences between these three mathematical relationships. y can increase as x increases, and the relationship doesn't have to be linear or proportional. Proportionality refers only to the special linear relationship where the y-intercept is zero, as shown in the example graph on the right.

6. MacMotion allows you to determine the relationship by trying various curves to see which best fits the plotted data. To fit the data on your graph of force probe reading vs. rubber band forces, select Fit . . . from the Analyze menu. To try



a linear fit, select Linear y = bo + b1*x and then press Try Fit.When you have found a good fit, where the curve goes through or close to all of the data points, print the graph along with the fit equation, and affix it in the space below.

Question 1-5: How are force probe readings related to the size of the pull exerted by the force probe hook on the rubber bands? Write down the equation you found and describe the mathematical relationship in words.

Question 1-6: Based on your graph, what force probe reading corresponds to the pull of one rubber band when stretched to your standard length? How did you determine this?

Comment: You can use your measurements to define a quantitative force scale. You might call it the "rubber band scale," or give it yours or your partner's name. Whenever the force probe has the reading corresponding to the pull of one rubber band stretched the standard length, the force is equivalent to one "rubber band," or one "Mary" or one "Sam." Any larger force can be measured as some number of these units. Your graph relates two different ways of measuring force, one with standard stretches of different numbers of rubber bands (rubber band units), and the other with a force probe. Such a graph is called a calibration curve and is used to compare measurements of quantities made with two different measuring instruments. You could use it to convert forces measured in force probe units to rubber band units, and vice versa. Physicists have defined a standard unit of force called the newton, abbreviated N. For the rest of your work on forces and the motions they cause, it will be more



Authors: David Sokoloff, Ronald Thornton & Priscilla Laws V1.40--8/94convenient to have the force probe read directly in newtons. Most spring scales have already been calibrated in newtons. All you need to do is to calibrate the force probe to read forces in newtons by using the spring scale to input two standard force measurements. If you have extra time, do the Extensions for Activity 1-2 now to examine the importance of a linear force scale like that of the spring scale. Activity 1-3: Calibrating the Force Probe Comment: The sensitivity of the force probe changes as the spacing between the magnet and the sensor is changed. The smaller the spacing, the more sensitive it is. The force probe will work better with the small applied forces you will use in the remainder of this investigation if you set the spacing to about 0.5 cm before calibrating. The best way to check the spacing is to check the sensitivity by looking at the raw data from the force probe before calibrating. 1. Be sure that the force probe spacing is about 0.5

cm, and that the lock nut is tight. Then, to check the sensitivity, select Calibrate Force . . . and then Raw Data from the Collect menu. Zero the force probe with nothing pulling on it. Start graphing and pull on the hook with a 2.0 N force applied with the spring scale. The reading on the graph (raw data) should be about 250-300. If it is not in this range, change the spacing, tighten the lock nut, Zero and check the reading again. When the reading with a 2.0 N pull is in the range 250-300, proceed with the calibration.

2. To calibrate the force probe, select Calibrate Force . . . from the Collect menu, then Calibrate Now, and follow the directions exactly. When the computer asks you to apply a known force to the force probe, pull on the hook with the spring scale, holding it with a steady 2.0 N reading on the scale. Enter this value in the space, continue to hold a steady reading, and press return. When the calibration is complete, you may release the spring scale.



3. Check the calibration. First Zero the force probe. Then Start recording data, and pull on the force probe with the spring scale with several different forces, each 2.0 N or smaller. Use Analyze Data A to record the force probe readings and corresponding spring scale readings in the table below.

Question 1-7: Do your force probe readings correspond to your spring scale readings? Can you now use the force probe to make reasonably accurate force measurements?



Authors: David Sokoloff, Ronald Thornton & Priscilla Laws V1.40--8/94 INVESTIGATION 2: MOTION AND FORCE

Now you can use the force probe to apply measured amounts of force to an object. You can also use the motion detector, as in the previous three units, to examine the motion of the object. In this way you will be able to establish the relationship between motion and force.You will need the following materials:

• MacMotion software (Motion for MS-DOS computers)

• RealTime Physics Mechanics Experiments folder• Force probe• Motion detector• Universal Laboratory Interface (ULI) • Spring scale with a maximum reading of 5 or 10

N• Cart or toy car with very little friction• Masses to increase cart's mass to about 1 kg• Smooth ramp or other level surface 2-3 meters

long• Low friction pulley, light weight string, table

clamp, variety of hanging massesActivity 2-1: Pushing and Pulling a CartIn this activity you will move a cart by pushing and pulling it with your hand. You will measure the force, velocity and acceleration. Then you will be able to look for relationships between the applied force and the motion quantities, to see which is (are) related to force.1. Set up the cart, force probe and motion detector on

a smooth level surface as shown below. The cart should have a mass of about 1 kg with force probe included. Fasten additional mass to the top if necessary.

The force probe should be fastened securely to the cart so that the handle does not extend beyond the



end of the cart facing then motion detector. Plug the force probe into port 1 of the ULI. The motion detector should be plugged into port 2. (Tape the cable from the force probe back along the handle to assure that it will not be seen by the motion detector.)

Prediction 2-1: Suppose you grasp the force probe hook and move the cart forwards and backwards in front of the motion detector. Do you think that either the velocity or the acceleration graph will look like the force graph? Is either of these motion quantities related to force? Explain. That is to say, if you apply a changing force to the cart, will the velocity or acceleration change in the same way as the force?

2. To test your predictions, open the experiment file called L3A2-1 (Motion and Force). This will set up velocity, force and acceleration axes with a convenient time scale of 5 sec, as shown below. Calibrate the force probe using a 2.0 N pull from a spring scale, if you haven't already done this in Activity 1-3.



Authors: David Sokoloff, Ronald Thornton & Priscilla Laws V1.40--8/94

3. Zero the force probe. Grasp the force probe hook and hit Start. When you hear the clicks, pull the cart away from the motion detector, and quickly stop it. Then push it back towards the motion detector, and again quickly stop it. Pull and push the force probe hook along a straight line--do not twist it. Be sure that the cart never gets closer than 0.5 m away from the detector.

4. Carefully sketch your graphs on the axes above, or print them and affix the graphs over the axes.

Question 2-1: Does either graph--velocity or acceleration--resemble the force graph? Which one? Explain.

Question 2-2: Based on your observations, does it appear that either the velocity or acceleration of the cart might be related to the applied force? Explain.



Activity 2-2: Speeding Up You have seen in the previous activity that force and acceleration seem to be related. But just what is the relationship between force and acceleration?Prediction 2-2: Suppose you have a cart with very little friction, and that you pull this cart with a constant force as shown below on the force-time graph. Sketch on the axes below your predictions of the velocity-time and acceleration-time graphs of the cart's motion.

PREDICTION

Describe in words the predicted shape of the velocity vs. time and acceleration vs. time graphs which you sketched.

1. Test your predictions. Set up the ramp, pulley, cart, string, motion detector and force probe as shown below. The cart should be the same mass as before (about 1 kg).




Be sure that the cart's friction is minimum. (If the cart has a friction pad, it should be raised so it doesn't contact the ramp.)

2. Prepare to graph velocity, acceleration and force. Open the experiment called L3A2-2 (Speeding Up) to display the velocity, acceleration and force axes shown on the next page.

3. It is important to choose the amount of the falling mass so the cart doesn't move so fast that you can't observe the motion. Experiment with different hanging masses until you can get the cart to move across the ramp in about 2-3 seconds after the mass is released. Also test to be sure that the motion detector sees the cart during its complete motion. Remember that the back of the cart must always be at least 0.5 meter from the motion detector.Record the hanging mass that you decided to use:

4. Calibrate the force probe with a force of 2.0 N applied to it with the spring scale if you haven't already done so. (Follow the procedure outlined in Activity 1-3 to set the spacing of the force probe before calibrating.)

5. Zero the force probe with the string hanging loosely so that no force is applied to the probe. Zero it again before each graph.

6. Single click on the velocity graph to graph velocity first. Start graphing. Release the cart after you hear the clicks of the motion detector. Be sure that the cable from the force probe is not seen by the motion detector, and that it doesn't drag the cart. Repeat until you get good graphs in which the cart is seen by the motion detector over its whole motion.



7. Move your graphs to Data B for comparison in the next activity.

FINAL RESULTS

8. If necessary, adjust the axes to display the graphs more clearly. Sketch the actual velocity, acceleration and force graphs on the axes above, or print the graphs and affix them over the axes. Draw smooth graphs; don't worry about small bumps.



Authors: David Sokoloff, Ronald Thornton & Priscilla Laws V1.40--8/94Questions 2-3: After the cart is moving, is the force which is applied to the cart by the string constant, increasing or decreasing? Explain based on your graph.

Question 2-4: How does the acceleration graph vary in time? Does this agree with your prediction? What kind of acceleration corresponds to a constant applied force?

Question 2-5: How does the velocity graph vary in time? Does this agree with your prediction? What kind of velocity corresponds to a constant applied force?



Activity 2-3: Acceleration from Different ForcesIn the previous activity you have examined the motion of a cart with a constant force applied to it. But, what is the relationship between acceleration and force? If you apply a larger force to the same cart (same mass as before) how will the acceleration change? In this activity you will try to answer these questions by applying different forces to the cart, and measuring the corresponding accelerations.If you accelerate the same cart (same mass) with one other force, you will then have three data points--enough data to plot a graph of acceleration vs. force. You can then find the mathematical relationship between acceleration and force. Prediction 2-3: Suppose you pulled the cart with a force about twice as large as before. What would happen to the acceleration of the cart? Explain.

1. Test your prediction. Keep the graphs from the previous activity in Data B.

2. Accelerate the cart with a larger force than before. To produce a larger force, hang a mass about two times as large as in the previous activity. Record the hanging mass:

3. Graph force, velocity and acceleration as before. Don't forget to Zero the force probe with nothing attached to the hook right before graphing.

4. Sketch your graphs as well as the graphs in Data B on the axes below or print out the graphs and affix them over the axes.

FINAL RESULTS




5. Measure the average force and average acceleration for the cart for this activity (Data A) and the previous activity (Data B), and record your measured values in the table on the top of the next page. Find the mean values only during the time intervals when the force and acceleration are nearly constant. (Select Analyze Data A or Analyze Data B from the Analyze menu. Click with the cursor on the force graph at the beginning of the time interval over which you want to find the mean force, and--while holding down the mouse button-- slide the cursor across to the end of the interval. This selected region on the graph should darken. Release the mouse, and then select Statistics . . . from the Analyze menu. The mean values of acceleration and force will be displayed.)



Question 2-6: How did the force applied to the cart compare to that with the smaller force in Activity 2-2?

Question 2-7: How did the acceleration of the cart compare to that caused by the smaller force in Activity 2-2? Did this agree with your prediction? Explain.

6. Accelerate the cart with a force roughly midway between the other two forces tried. Use a hanging mass about midway between those used in the last two activities.Record the mass:

7. Graph velocity, acceleration and force. Sketch the graphs on the axes on page 3-15, or print and affix them.

8. Find the mean acceleration and force, as before, and record the values in the table.

If you have time, carry out the Extensions for Activity 2-3 now to get more data for the acceleration vs. force graph you will make in the next activity.

Activity 2-4: The Relationship Between Acceleration and Force.In this activity you will find the mathematical relationship between acceleration and force.



Authors: David Sokoloff, Ronald Thornton & Priscilla Laws V1.40--8/941. Plot a graph of acceleration vs. force from the data

in the table. To plot the graph using the MacMotion software, load the experiment L3A2-4 (Acceleration vs. Force). Double click on the first row of the Average Force column and then enter the average force data points. The return key will move you down the column. Do the same for average acceleration. The data will be plotted as you enter the values. You may wish to change the graph axes, after all of the data are entered, to better display the data.

2. Determine the mathematical relationship between the acceleration of the cart and the force applied to the cart as displayed on your graph. Use Fit . . . on the Analyze menu as you did in Activity 1-2 on page 3-6.

3. Print your graph along with the fit equation, and affix it in the space below.

Question 2-8: Does there appear to be a simple mathematical relationship between the acceleration of a cart (with fixed mass) and the force applied to the cart (measured by the force probe mounted on the cart)? Write down the equation you found and describe the mathematical relationship in words.

Question 2-9 If you increased the force applied to the cart by a factor of ten, how would you expect the acceleration to change? How would you expect the acceleration-time graph of the cart's motion to change? Explain based on your graphs.



Question 2-10: If you increased the force applied to the cart by a factor of ten, how would you expect the velocity-time graph of the cart's motion to change? Explain based on your graphs.

Comment: The relationship which you have been examining between the acceleration of the cart and the applied force is known as Newton's Second Law.



Authors: David Sokoloff, Ronald Thornton & Priscilla Laws V1.40--8/94EXTENSIONS FOR LABORATORY 3: FORCE AND MOTION

Extensions for Activity 1-2: Importance of Linear Force ScalesYou have probably observed in Activity 1-2 that the a force scale based on the force probe is approximately a liner one. That is, if you apply twice as large a force (e.g., by pulling two rubber bands rather than one to the standard length) the force probe gives just about twice the reading. Not all devices give a linear force scale.Use the force probe to examine the force scales produced by 1) a single rubber band and 2) a spring stretched to various lengths. That is, set up experiments to graph the force applied as a function of length for each of these. Based on your graphs, is either of these force scales linear? What are the advantages of using a linear force scale?

Extensions for Activity 2-3: More Acceleration vs. Force DataGather data for average acceleration and average force for several other forces applied to the same cart. Add additional rows to the data table on page 3-16. Plot a graph of average acceleration vs. average force for all of the data collected.



TEACHERS' NOTES FOR LABORATORY 3: FORCE AND MOTION

Equipment and Materials• MacMotion software (Motion for MS-DOS computers)• RealTime Physics Mechanics Experiments folder• Force probe• Universal Laboratory Interface (ULI) • Five identical rubber bands• Meter stick• Spring scale with a maximum reading of 5 or 10 N• Smooth ramp or other level surface 2-3 meters long• Cart or toy car with very little friction• Masses to increase cart's mass to about 1 kg• Low friction pulley, light weight string, table clamp,

variety of hanging masses

The design of the force probe is based upon the use of a Hall effect transducer to measure changes in magnetic field. The transducer is mounted in the handle of the probe, directly opposite to the magnet. The magnet is mounted on a flexible diaphragm with a hook on the opposite side. When the hook is pushed or pulled, the distance of the magnet from the Hall transducer changes, thus changing the magnetic field in the vicinity of the transducer. This change in field is transformed to a change in Hall voltage, and this is ultimately displayed as a change in force displayed on the computer. The spacing between the magnet and the Hall transducer of the Force Probe should normally be about 3/4 cm. For measuring smaller forces, it may be better to make the probe more sensitive by decreasing this distance, and then re-calibrating the force probe. The best way to assure that the spacing (and sensitivity) is set right is to check the raw data from the force probe when the largest force you will measure is applied to it. The procedure, as outlined in Activity 1-3, is as follows. Set the force probe spacing , and tighten the lock nut. Then, select Calibrate Force . . . and then Raw Data from the Collect menu. Zero the force probe with nothing pulling on it. Start graphing and pull on the hook with the maximum force which will be applied during the experiment. The reading on the graph (raw data) should be about 250-300. If it is not in this range adjust the sensitivity by changing the spacing and tightening the lock nut. Zero the force probe



Authors: David Sokoloff, Ronald Thornton & Priscilla Laws V1.40--8/94and then check the reading with the maximum applied force again. When the reading with the maximum pull is in the range 250-300, proceed with the calibration.Always be sure that the probe is not saturating--indicated by a flattening out of the force graph even as the applied force is increased. If this occurs, increase the spacing, and re-calibrate.The force probe is temperature sensitive, and has a tendency to drift a bit. It should be zeroed with no force applied to the hook before each measurement (by pushing the ZERO button with the mouse).The rubber bands must be chosen so that five can be stretched to a reasonable length without saturating the force probe. You will also need to select matched sets.

The best spring scales are the plastic tubular ones with an adjustable zero. They are available from a number of suppliers for about $5 apiece, for example Central Scientific #31266, 31267 or 31268. The maximum reading should be 5 or 10 N.

The motion detector is described in the Equipment and Materials section of the Teachers' Notes for Lab 1, and the force probe, cart and ramp are described in Equipment and Materials section of the Teachers' Notes for Lab 2. In general you should raise whatever ramp you are using to get a 1.5 m height for the weight to fall through. The lightweight PASCO ramp can easily be raised above the table. If you are not using a PASCO ramp and you are having difficulty getting 1.5 m off the floor, you can use the arrangement shown in Figure 1.The disadvantages of this arrangement are that it doesn't look straightforward to students, it requires two pulleys, and mis-aligned pulleys can cause substantial frictional forces.



Activity 2-1 will work best if the cart is weighted down to at least 1 kg. Give a short push in one direction, pause, then a short pull back in the other direction, pause, then repeat. Try not to torque the hook on the force probe, as this will give false readings.The activities in which the cart is accelerated using the modified Atwood's machine are also more easily done if the cart has a mass of about 1 kg. Then a reasonable hanging mass can be used, and this results in a force which can be accurately measured with the force probe. Also, it is important that the motion of the cart be on a time scale such that the students can actually see that it is accelerating as it moves across the ramp. Thus, even with a 1 kg cart, the applied force is still a fairly small one, and it is very important that attention be paid to the following:1. Be sure that the spacing between the magnet and the

force probe sensor is small enough so that the force probe is sensitive enough to measure the applied forces accurately. A spacing of 0.5 cm or smaller is appropriate for these activities. This may necessitate changing the spacing and re-calibrating after the rubber band activities. Use the procedure outlined above and in Activity 1-3.

2. Zero the force probe with no force applied to it before each measurement.

Finally, it is important that the motion detector see the end of the cart and not the force probe or cable, which may be seen as intermittent targets. This means mounting the force probe on the cart so that the handle does not extend beyond the end of the cart seen by the motion detector, and keeping the force probe cable off to the side or above the cart. It is



Authors: David Sokoloff, Ronald Thornton & Priscilla Laws V1.40--8/94helpful to tape the cable back along the force probe handle. Care in setting up the cable will also avoid any drag on the cart as it moves along. If the motion detector is not seeing the cart consistently, mounting a card on the end of the cart may help. However, this card must be rigid so that it does not wave in the air as it moves.

Sample Graphs

Figure 2 shows the force values measured by the force probe plotted above the number of rubber bands which are stretched to the same standard length, thus allowing the force probe to be calibrated in "rubber band" units, as in Activity 1-2. Figure 3 shows a linear fit to these data using the Fit routine in MacMotion. It is essential that the rubber bands be matched, and that they are all stretched to the same length. It is also essential that the force probe be calibrated with the appropriate separation and applied force so that it does not saturate.

The y-intercept in the fit equation is about 0.6, and the standard deviation in this value (found in Fit Results . . . on the Analyze menu) is 0.8, indicating that within experimental uncertainty, the relationship is a directly proportional one.Figure 4 shows the velocity, force and acceleration graphs for the starting and stopping motion of a cart with a force probe mounted on it, as in Activity 2-1. With the force probe hook grasped, the cart



Figure 4: Velocity, force and acceleration graphs for a cart pulled away from the motion detector beginning at about 0.5 sec and then quickly stopped, then pushed back toward the motion detector beginning at about 2.2 sec and again quickly stopped, as in Activity 2-1.



Authors: David Sokoloff, Ronald Thornton & Priscilla Laws V1.40--8/94was pulled away from the motion detector and then quickly stopped. After a second or so, it was then pushed back toward the motion detector and quickly stopped. As can be seen, the shape of the acceleration graph is very similar to the force graph, while that of the velocity graph is quite different. This is suggestive that acceleration and force--and not velocity and force--are related to each other. This relationship appears most dramatic when the pulls and pushes are most abrupt and of very short duration. Figure 5 shows velocity, acceleration and force graphs for a cart accelerated b y a constant applied force as in Activity 2-2.

Figure 5: Velocity, acceleration and force graphs for a low friction cart accelerated by a constant applied force as in Activity 2.2. At the end of the track, the cart was stopped by colliding with a bumper.

The constant acceleration region is roughly between 0.6 sec and 2.2 sec. The large negative dip in the acceleration after 2.4 sec is caused by the collision with the end bumper of the track. This force is not seen on the force graph, since the force probe did not collide with the bumper. The following suggestions may help you to troubleshoot any problems with your graphs.

1. If the velocity graph levels out, the motion detector is probably not seeing the cart to the end of the track. Check for objects alongside the track which may be seen by the motion detector. Use Analyze Data A to find out the distance of this obstruction from the motion detector, and rearrange the setup so that it is



no longer interfering. It may be necessary to tilt the motion detector slightly to one side or slightly upward.

2. If your graphs aren't as smooth as these, your track may have rough spots, the bearings on your cart may be bad or the motion detector may be seeing the force probe cable or the force probe handle and the end of the cart intermittently. To correct the latter, move the force probe so that the handle doesn't extend beyond the end of the cart, and position the cable out of the way. Taping a stiff cardboard card to the end of the cart may also help.

3. If the acceleration changes as the cart moves along, it may be that the force probe cable is dragging. Suspend or hold the cable above the cart so that the cart can move freely without being pulled by the cable.


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