name: prelab forces and motion - dartmouth...

Name: ______________________________ Forces and Motion, p. 1/11

Adapted from RealTime Physics (Sokoloff et al.) for P13 Revised: 1/2004

PRELAB: FORCES AND MOTION

1. What is the purpose of the rubber bands in Activity 1-1?

2. What is the difference between a linear relationship and a proportional one?

3. Sketch Prediction 2-2 on the set of axes below. Explain the reasons behind your prediction.

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FORCE AND MOTION

Topic: Newton’s Laws in 1D

Objectives:

• To quantify “pulls” and “pushes”

• To identify the effect that “pulls” have on the motion of an object

• To find the mathematical relationship between the force applied to it and its acceleration

• To critically examine the inferences that can (and can’t) be drawn from observations Overview:

In previous labs, you have used a motion detector to display position, velocity and acceleration graphs of various objects moving in one dimension. You were not concerned about how you got the objects to move, i.e. what pushes or pulls acted on the objects. From your own experiences, you know that amount of pull or push and motion are related in some way. You’ve probably also heard in lecture that the acceleration an object undergoes is proportional to force acting on the object. This mathematical statement, often called Newton’s 2nd law, can be taken as Newton’s definition of force. Because of the similarities between Newton’s mathematical definition of force and our notions about pushes and pulls, it seems natural to conclude that our simplistic notion of “pull” and “push” corresponds exactly to the word “force” in Newton’s law. This lab examines whether this assumption is a reasonable one. This will be done in two steps. You will first develop a way to measure “pulls.” You will then examine how the motion of a cart is related to the amount of pull being exerted on it.

There are two educational purposes for this lab. The most obvious purpose is to give you some intuitive sense about the relationship between pulls/pushes and motion. The second, far less obvious, educational goal is acquaint you with some of the issues involved in developing/testing ideas about the world. Throughout this lab, you will critically examine what claims can be substantiated by the experimental evidence you collect.

Safety/Equipment Notes:

Mounting Hardware: Your TA will demonstrate how to attach the force probe to the cart.

Do not allow the cart crash into the pulley! Before you start each run, make sure someone is ready to stop the cart at the far end of the track.

Strong pushes and pulls may damage the force probes. The probes are rated for a maximum of 50 N.

Writing it up:

In this handout, you will be asked to perform calculations, analyze graphs and answer questions. It is strongly recommended that you do all the calculations and answer all the questions as you go through the experiment. This record is for your purposes only. You will not be graded on it. You will be graded on how well you understand the material covered in this lab, so you should do the entire activity, discuss the questions with your partners and take careful notes.



Investigation 1: Measuring Pulls

In this investigation, you will learn how to construct a QUANTITIVE scale for measuring the amount of pull.

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 a meter stick to the table. Now stretch the rubber band so that it is a 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 blow. This will be your standard length for future measurements.

Standard length of rubber band = _________ cm

3. Attach one end of each of two identical rubber bands to some thing that can’t move and stretch them together side-by-side to the standard length.

Q1-1: How does the combined pull of two rubber bands compare to what you felt when only one rubber band was used?

4. Repeat this comparison of how strong the pull feels with three, four and five rubber bands stretched together to the same standard length.

Q1-2: Suppose you stretched a rubber band to your standard length by pulling on it. Now you want to create a pull six times as large. How could you create such a pull?

Q1-3: Suppose you applied a pull with a stretched rubber band one day, and several days

later you wanted to feel the same pull or apply it to something. How could you assure that pulls were the same? Explain.

Q1-4: Do side-by-side rubber bands provide a convenient way of accurately reproducing

pulls of many different sizes? Explain.

You have seen that pulling more rubber bands to the same length requires a larger pull. To be more precise about the pulls and pushes you are applying, you need a device to measure these pulls accurately.

Activity 1-2: Measuring “Pulls” with an Electronic Probe

In this activity you will explore the capability of an electronic probe as a measuring device for “pulls.”



1. Plug the probe into the computer and start the software. Use the software to set the probe to “pull positive” and fastest sampling rate possible. Display force* vs. time axes.

2. Zero the probe with nothing pulling on it. The probe should lie flat on the table.

3. Attach one end of a rubber band to something that 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 rubber band is stretched to the same standard length you used in Activity 1-1, and begin graphing while holding the rubber band steady for the whole graph. Use the software to get an accurate reading of the force.

Record a typical force reading: ____________

4. Repeat the previous step with different number of rubber bands, arranged side-by-side, as in Activity 1-1. Record the results in the table below:

Number of rubber bands 0 1 2 3 4 5

Probe reading

Comment: We are interested in the nature of the mathematical relationship between the reading of the force probe and the force (in rubber band units). This can be determined from a graph of the data above by drawing a smooth curve that 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 types of mathematical relationship. y can increase as x increases, and the relationship doesn’t have to be linear or proportional. Proportionality refers to the special linear relationship where the y intercept is zero, as shown in the example graph at the right.

“Zeroing” the probe: The electrical signal the probe generates can drift with time, temperature and other factors. Pressing the zero button resets the output of the probe to zero. This process is called “zeroing.”



5. Use the software to create a chart of the data above. Use the chart to make a graph of the data. Then use the fit routine in the software to find the relationship that best fits the plotted data. Try a linear fit and any other fit you think is appropriate. When you have found a good fit, print the graph and the fit equation. Write the fit equation in the space below:

Fit Equation: ________________________ Q1-5: Is it fair to say that the probe output is proportional to the amount of pull on the

hook? Explain. Q1-6: Suppose the probe output was not proportional to the amount of pull. Could the

probe still be used to measure “pull”? Would it be as convenient? Explain. Q1-7: Based on your observations so far, is it possible to identify the quantity that the

probe measures as the “force” referred to in Newton’s laws?

è Check your answers with an instructor.

Investigation 2: Motion and Force

Now you can use the probe to apply pulls with known strengths to an object. You can also use the motion detector, as in the previous two labs, to examine the motion of the object. In this way you will explore the relationship between motion and “pull.”

Activity 2-1: Pushing and Pulling a Cart

In this activity you will move a low friction cart by pushing and pulling it with your hand. You will measure the probe output, velocity and acceleration. Then you will look for mathematical

Comment on units and calibration: You can use your measurements to define a quantitative “pull” scale. You might call it the “rubber band scale” or name it after yourself or your lab partner. Whenever the probe has the reading corresponding to the pull of one rubber band, the “pull” is equivalent to one “RBU” (i.e. one rubber band unit), or one “Mary” or one “Sam.” Any larger pull can be measured as some number of these units.

Your graph relates two different ways of measuring pull, one with standard stretches of different numbers of rubber bands (RBU’s) 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 methods.

Physicists have defined a standard unit of pull called the newton, abbreviated N. For the rest of your work on forces and the motions they cause, it will be more convenient to have the probe measure directly in newtons. Then the pulls you measure can be compared to the forces everyone else measures. All that needs to be done is to calibrate the probe to read forces in newtons. This has been done by the manufacturer. The calibration can be checked using applying pulls with known strengths to the force probe (such as with a spring scale or by handing weights from the probe hook).



relationships between the probe output and the velocity and acceleration, to see whether either is (are) related to probe output.

1. Set up the cart, 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. The force probe should be fastened securely to the cart so that the cart’s body and cable do not extend beyond the end of the cart facing the motion detector.

Prediction 2-1: Suppose you grasp the probe hook and move the cart forward and backward in front of the motion detector. Do you think either the velocity or the acceleration graph will look like the “pull” graph? Is either of these motion quantities related to “pull”? (That is to say, if you apply a changing pull to the cart, will the velocity or acceleration change in the same way as the probe output? Explain the basis for your prediction.

2. To test your predictions, plug in the motion detector. Use the software to set the motion

detector up to measure velocity and acceleration at the maximum possible sampling rate. Display axes for velocity, force and acceleration. Make sure the time axes for the three graphs are aligned vertically as shown below.

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3. Zero the probe. Grasp the probe hook and begin graphing. When you hear the clicks, quickly pull the cart away from the motion detector and quickly stop it near the far end of the track. Then quickly push it back toward the motion detector and again quickly stop it. Pull and push the force probe hook along a straight line parallel to the track.

4. Carefully sketch your graphs on the axes above, or print them out and label them.

Q2-1: Does either graph –velocity or acceleration— resemble the force graph? Which one? Explain how you reached this conclusion.

Q2-2: Based on your observations, does it appear that there is a mathematical relationship

between probe output (i.e. amount of “pull”) and velocity, probe output and acceleration, both, neither? Explain.

Activity 2-2: Speeding up again

You have seen in the previous activity that probe output and acceleration seem to be related. But just what is the relationship between probe output and acceleration? In this activity, you will examine what happens as a cart pulled by a string accelerates.

Prediction 2-2: Suppose that you have a cart with very little friction and you pull this cart with a constant amount of “pull” as shown below on the force-time graph. On the axes below, sketch your predictions of the velocity-time and acceleration-time graphs of the cart’s motion.

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1. Test your predictions. Set up the ramp, pulley, cart string motion detector and probe as shown below. The cart should be the same mass as before. Be sure the cart’s friction is at a minimum. (If the cart has a friction pad, it should be raised so it doesn’t contact the ramp.) Prepare to graph velocity, acceleration and force. (If you’ve followed the directions to this point, this should already set up).

2. It is important to choose the amount of falling mass so that the cart doesn’t move too fast to

observe the motion. Experiment with different hanging masses until you get the cart to move across the track in about 1-2 sec after the mass is released.

Record the hanging mass that you use: ____________ (Don’t forget the units)

Also test to make sure that the motion detector “sees” the cart throughout the motion.

3. Zero the force probe with the string hanging loosely so that no force is applied to the probe. Zero the probe before each run.

4. 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 or pull the cart. Repeat until you get good graphs over its whole motion. Keep this data on the screen. You will need it for Activity 2-3.

5. Carefully sketch your graphs on the axes above, or print them out and label them.

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Q2-3: After the cart is moving, is the amount of “pull” applied to the cart by the string constant, increasing, or decreasing? Explain based on your graph.

Q2-3: How does the acceleration graph vary with time? Does this agree with your

prediction? Does a constant “pull” produce a constant acceleration?

Q2-4: How does the velocity vary in time? Does this agree with your prediction? What kind of change in velocity corresponds to a constant applied “pull”?

Q2-4a: Based on your observations so far, is it possible to identify the quantity that the

probe measures as the “force” referred to in Newton’s laws? Explain.


Activity 2-3: Acceleration from different forces

In the previous activity you examined the motion of a cart with a constant amount of “pull” applied to it. But what is the mathematical relationship between “pull” and acceleration? If you apply a larger pull to the same cart (while the mass of the cart is not changed) how will the acceleration change? In this activity you will try to answer these questions by applying different pulls to the cart and measuring the corresponding accelerations.

Prediction 2-3: Suppose that you pulled the cart with a pull about twice as large as before. What would happen to the acceleration of the cart? Explain.

1. Test your prediction. Keep the graphs from Activity 2-2 displayed on the screen. 2. Accelerate the cart with a larger force than before. To produce a larger force, hang a mass about

twice as large as in the previous activity.

3. Record the hanging mass: __________ (Don’t forget units)

4. Graph force, velocity, and acceleration as before. Don’t forget to zero the force probe with nothing attached to the hook before graphing.

5. Sketch your graphs as well as the graphs from Activity 2-2 on the axes on the next page, or print them out and label them.

6. Use the analysis tools of the software to determine the average pull and average acceleration for the cart in this activity and Activity 2-2, and record the values in the table below. Note: To find the average pull, you will probably want to use the statistics feature on the graph of the probe’s output; to find the average acceleration, you may want to use the fit tools on the velocity graph… Make sure that you only consider the time intervals when the force and acceleration were nearly constant.



Average Force (N) Average Acceleration (m/s2)

Activity 2-2

Activity 2-3

Q2-5: How did the force applied to the cart compare to that with the smaller force in

Activity 2-2?

Q2-7: How did the acceleration of the cart compare to that caused by the smaller force in Activity 2-2? Does this agree with your prediction? Explain.

Activity 2-3: Relationship between acceleration and force

1. Gather data for average acceleration and average force for several other forces applied to the same cart. Complete the table on the previous page.

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FINAL RESULTS: Activity 2-2 and Activity 2-3



2. Use the software to create a graph of the data in the table. Use the fit routine to determine the mathematical relationship between the acceleration of the cart and the force applied to the cart.

3. Print the graph with the fit equation and label it.

Q2-8: Does there appear to be a simple mathematical relationship between the acceleration of a cart (with fixed mass and negligible friction) and the amount of pull measured by the probe? Write down the equation you found and describe the mathematical relationship in words.

Q2-9: If you increased the force applied to the cart by a factor of 10, how would you expect the acceleration-time graph of the cart’s motion to change? Explain based on your graphs.

Q2-10: If you increased the force applied to the cart by a factor of 10, how would you expect the velocity-time graph of the cart’s motion to change? Explain based on your graphs.

Q2-12: Based on your observations so far, is it possible to identify the quantity that the

probe measures as the “force” referred to in Newton’s law? Explain. Q2-13: What is the value of the slope of the force-acceleration graph? How does this value

compare to the mass of the cart (as measured by a balance)? Q2-14: Based on your observations so far, it is possible to conclude that the slope of the

force-acceleration graph and the mass represent the same quantity? If so, explain how the observations you have made so far support the conclusion. If not, describe an experiment that could be used to help substantiate this claim.


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