Force and Acceleration
5. Force and Acceleration*
This unit has to do with how force changes the state of motion. The problems involve a fan cart, which is
a low-friction cart accelerated along a track by a fan or propeller, as you see in the figure.
Learning Objectives:
1. See qualitatively how forces and mass control
the change of an objects velocity.
Air
Flow
2. Connect the statements of Newton’s laws with
graphs of position or velocity versus time, or
acceleration versus mass or force.
Force
Reading: Before lab, read about Newton’s three laws
of motion, how weight is related to mass, the normal
force, and the force of friction for surfaces in contact.
Read the following sections. (Section numbers may be
slightly different depending on the edition of your
textbook: Check the section titles.)Study the following
sections of your textbook before coming to lab. There
will be a check to see that you have done this.
Knight Jones & Field (161): 4.6 Newton's Second Law, 5.2 Dynamics and Newton's Second Law,
Serway and Vuille (211): 4.3: Newton's Second Law
Serway and Jewett (251): 5.4 Newton’s Second law
PRE-LAB EXERCISES
Before coming to lab, answer the following prediction questions 1 through 7. At the beginning of
lab, your TA will check to see that you have them done. You will hand in the pre-lab work later as part of
your lab report.
A
The finger pushes two
blocks along the bench.
The mass of A is 3 kg
and the mass of B is 2
kg.
B
The blocks start from rest. Suppose there is no friction. The finger pushes with constant force for one
second. At the end of this time the blocks are moving at 2 meters per second.
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*© William A Schwalm 2012
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Force and Acceleration
1. How much force must the finger exert on block A?
2. How much force must block A exert on block B and in which direction?
3. How much force must block B exert on block A and in which direction? Which physics law leads you to
this conclusion?
4. Initially, the lower left corner of block A is at the origin x = 0. Draw a graph of the position of the lower
left corner of block A as a function of time for times between t = 0 s and t = 1 s.
1.0 m
.8 m
.6 m
.4 m
.2 m
.2 s
.4 s
.6 s
.8 s
1.0 s
5. Draw a graph of the velocity versus time, for times from t = 0 s to t = 2 s. (Provide your own axes with
appropriate scales.) Note that the finger stops pushing at t = 1 s.
6. Suppose on a low friction track, when the fan is set to its low setting, the fan cart accelerates a
total mass (cart plus load) of 3 kg from zero to 1 m/s in 6 seconds.
a. How much thrust (accelerating force) is exerted on the cart by the action of the fan?
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Force and Acceleration
b. Suppose that on the high setting, the fan cart with the same load accelerates from zero to
1 m/s in 1.5 seconds. How much thrust does the fan produce now?
3. There will actually be some friction in the wheel bearings. What variables do you think the
frictional force will depend on? Can you guess a formula for this force?
Equipment: Fan cart with two-speed motor and propeller with adjustable direction. (Safety tip: Don’t get
your fingers in the way of the fan.) 2.2 meter aluminum track. (Don’t lean on the tracks or pile stuff on
them, because if you bend them even a tiny bit they are ruined. They cost more than you want to pay.)
Two loadable, low-friction carts with magnetic bumpers. Video camera, meter stick, computer and
Logger-Pro software. There are some extra weights for loading up the low-friction carts. In the room
there are also some tubular force scales for measuring force, blue tape, a carpenter’s level, a triple beam
balance for measuring mass, some pulleys, string and weight hangers you might want to use. Remember
that the computers have a scientific calculator under Accessories on the All Programs menu attached to
the start menu.
Exploration: Try out the fan carts. You can use them to push the low-friction carts, which can carry extra
weight. The track may be level or not. You can mess around with the angle of the fan, and so on. Your
group will need to figure out a plan for taking video data. Everyone in your group has to get his or her
hands involved in making the measurements, so here is where you learn how things work.
With the motor off, place the cart on the track and give it a gentle shove. How would you describe the
motion during the time after the cart leaves your hand and when it stops?
Try taking some position versus time and velocity versus time data. If you have two different members
from your group capture data from the same video by clicking on the cart image in the video, it would be
interesting to see how much difference there is in the two sets of velocity data. What does this tell you
about the measurements?
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Force and Acceleration
Problem 1 Effect of varying force
Your group needs to plan a set of experiments to study the effect of changing the applied force, the thrust
from the fan.
1. Method Question: Think of a plan, using the available materials, to measure the thrust of the propeller
(i.e. force on the fan cart due to the air blown by the propeller) for both the high and low settings of
the motor switch. Later, you are going to relate this thrust to motion, so you should not use motion of
the cart to determine the force initially.
2. Prediction Question: What mathematical relationship do you expect to find between the thrust and the
motion of the cart? Why do you expect this? Also, sketch a graph predicting how the velocity of the
fan cart, starting from rest, should vary with time for (a) the low fan speed, and (b) the high fan speed.
Comment on the slopes.
Plan: You need to plan experiments to actually determine the effect of the thrust on the motion of the cart.
Develop a simple outline for a measurement plan, and show this plan to your TA before you begin taking
data. Record the plan outline here. As part of it, indicate what data you need and/or what data tables
you should make and what graphs you should create.
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Force and Acceleration
Implementation: Perform the measurements. Assign different parts of the measurement task to different
group members. Everyone’s hands should be busy, and in case the TA asks, everyone should know
what’s going on. Record the relevant data here, and attach copies of the most relevant graphs.
Analysis: Using the tools available, analyze your data in a way that let’s you compare to your predictions.
Summarize your analysis here and show the results. If relevant, attach figures, graphs or other computer
output, and explain here what you see in the attachments. You need to be explicit, although you
shouldn’t be too verbose.
Conclusions: What did you learn?
1. Consider the following first qualitatively (in terms of general trends of graphs and ball-park figures)
and then quantitatively (in terms of comparing numbers). Did the results agree with your group’s
predictions qualitatively?
Then secondly, how well did your results and predictions agree
quantitatively? I’m looking for an actual value here for how good the agreement was, so you know
you have to explain also how you came up with this.
2. What causes the quantitative disagreement? First, what do you think is the main measurement
error? Then, besides measurement errors, what could be going on here that you didn’t take into
account?
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Force and Acceleration
Problem 2 Effect of varying mass
Now the group needs to plan some experiments to study the effect of changing the mass, keeping the
thrust from the fan constant. (Note: It is best not to try to place iron masses on the magnetic deck of the
fan cart, as they slam into the propeller when the cart hits the bumper at the end of the track.)
1. Method Question: You need a way of having the fan accelerate different, known amounts of mass
and to analyze the motion via video capture. As noted immediately above, you cannot load weights
directly on the fan cart. How can you set up an experiment where you can vary the mass
conveniently?
2. Prediction Question: What mathematical relationship do you expect to find between the mass and
the motion of an object? What makes you think so, that is, what physical principle is involved here?
Also, sketch two graphs on the same axes predicting how the velocity, starting from rest, should vary
with time for the fan on low speed and (first graph) a lighter total mass, and (second) heavier mass.
Comment on the slopes.
Plan: Make a plan for studying the way the motion depends on mass when the applied force is kept
constant. Decide on a plan, white an outline here, and check it out with your TA before going further. Be
sure to indicate what needs to be measured, what video data should be analyzed, and how.
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Force and Acceleration
Implementation: Perform the measurements. Assign different parts of the measurement task to different
group members. Again everyone’s hands should be busy, and everyone should know what the heck is
going on. Record the data you need here, and attach copies of any appropriate graphs.
Analysis: Using the tools available, analyze your data so as to compare to your predictions. Summarize
the analysis here with a few sentences. Attach whatever figures, graphs or other computer output you
need in order to explain. Describe what you see in the attachments. Be explicit but concise.
Conclusion: What did you learn?
1. Regarding the effect of changing mass: Did the results agree with your group’s predictions
qualitatively? Then secondly, how well did they agree quantitatively?
2. What two types of factors do you figure caused the quantitative disagreement? First, what about
measurement error? Then, besides measurement errors, what else could be going on?
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Force and Acceleration
Problem 3: Effect of friction
Now we need to face the fact that in the real world, even low-friction bearings do have some friction. How
can we account for this?
1. Prediction question: From what you know about the relationship between forces and motion: how do
you expect friction to affect the results? If you just gently pushed and released a fan cart with the
motor off, what should happen?
2. Method question: Therefore, how can you use video data to estimate the frictional force from the
bearings?
3. Prediction question: How do you figure frictional force should depend the speed of the cart, loading of
the cart, etc? List the factors you think should be involved and indicate for each one whether it
should increase or decrease the frictional force. Finally, your group should try to develop a formula
for the frictional force from the wheel bearings. See what you come up with. (Watch the dimensions.)
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Force and Acceleration
Plan: You need to plan experiments to actually determine the effect of friction in the wheel bearings. As
part of it, you will need to state the formula or hypothesis you are working on. Then you should indicate
what data you need and/or what data tables you should make and what graphs you should create. Write
an outline for a measurement plan, and show this plan to your TA before you begin taking data.
Implementation: Now take the necessary data, including video capture, in implement your plan. As
always, everyone should be involved in taking the data. Record the necessary procedural notes and the
relevant, non-video data here.
Analysis: Using the tools you have, analyze the data to see whether they support your theory. As you
know, there are two levels of agreement: qualitative and quantitative, so your analysis should look for
both or either type. (For qualitative studies, sometimes a graph is best. What graph would be most
useful here?) Show the results of your analysis. You may want to attach a graph, but be sure to explain
what it shows.
Conclusions: Do your measurements support your theory qualitatively?
quantitative agreement? Are there any strange surprises in any of the data?
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To what extent is there
Force and Acceleration
Summary: At the end of the lab unit, your group will be asked to respond to the following questions.
They are really asking you what the point of the lab unit is. Jot down your own answers here, after
consulting with your group.
1. What laws or principles of physics that you have learnt from your reading or from lecture do these
three problems actually address?
2. What other things did you learn from doing the exercises?
Reference
1. “Fan cart physics,” by Robert Morse in The Physics Teacher
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