Slide 1
LAB 9: WORK AND ENERGY
Please list the members of your group:
Madisyn Burwell
OBJECTIVES
To extend the intuitive notion of work as physical effort to a formal mathematical definition of
work, W, as a function of both the force on an object and its displacement.
To develop an understanding of how the work done on an object by a force can be measured.
To understand the concept of power as the rate at which work is done.
To understand the concept of kinetic energy and its relationship to the net work done on an object
as embodied in the work–energy principle.
OVERVIEW
In your study of momentum, you saw that while momentum is always conserved in collisions,
apparently different outcomes are possible. For example, if two identical carts moving at the same
speed collide headon and stick together, they both end up at rest immediately after the collision. If they
bounce off each other instead, not only do both carts move apart at the same speed but in some cases
they can move at the same speed they had coming into the collision. A third possibility is that the two
carts can “explode” as a result of springs being released (or explosives!) and move faster after the
interaction than before.
Two new concepts are useful in further studying various types of physical interactions—work and
energy. In this lab, you will begin the process of understanding the scientific definitions of work and
energy, which in some cases are different from the way these words are used in everyday language.
You will begin by comparing your intuitive, everyday understanding of work to its formal mathematical
definition. You will first consider the work done on a small pointlike object by a constant force. There
are, however, many cases where the force is not constant. For example, the force exerted by a spring
increases the more you stretch the spring. In this lab you will learn how to measure and calculate the
work done by any force that acts on a moving object (even a force that changes with time).
Often it is useful to know both the total amount of work that is done, and also the rate at which it is
done. The rate at which work is done is known as the power.
Energy is a powerful and useful concept in all the sciences. It is one of the more challenging concepts
to understand. You will begin the study of energy in this lab by considering kinetic energy—a type of
energy that depends on the velocity of an object and on its mass.
By comparing the change of an object’s kinetic energy to the net work done on it, it is possible to
understand the relationship between these two quantities in idealized situations. This relationship is
known as the work–energy principle.
You will study a cart being pulled by the force applied by a spring. How much net work is done on the
cart? What is the kinetic energy change of the cart? How is the change in kinetic energy related to the
net work done on the cart by the spring?
Copyright © 2018 John Wiley & Sons, Inc.
Slide 2
INVESTIGATION 1: THE CONCEPTS OF PHYSICAL WORK
AND POWER
While you all have an everyday understanding of the word “work” as being related to expending effort,
the actual physical definition is very precise, and there are situations where this precise scientific
definition does not agree with the everyday use of the word.
You will begin by looking at how to calculate the work done by constant forces, and then move on to
consider forces that change with time.
Let’s begin with a prediction that considers choosing among potential “reallife” jobs. Suppose you are
president of the Load ‘n’ Go Company. A local college has three jobs it needs to have done and it will
allow your company to choose one before offering the other two jobs to rival companies. All three jobs
pay the same total amount of money.
Prediction 11A: Which one would you choose for your crew?
Job A
Prediction 11B: Explain why.
Job B
Job C
Slide 3
Activity 1-1: Eﬀort and Work—Calculating Work
The following activities should help you to see whether your choice makes the most sense. You will
need the following:
IOLab: make sure you calibrate the force sensor!
two heavy books of approximately the same weight
smooth board or other level surface at least 0.5 m long that can be inclined
meter stick or measuring tape
string
protractor
1. Lift one of the books at a slow, constant speed from the floor to a height of about 1 m. Repeat
several times. Note the effort that is required.
2. Repeat, this time lifting the two books 1 m.
3. Push a book 1 m along the floor at a constant speed. Repeat several times.
4. Repeat, this time piling two books on top of each other and pushing them 1 m.
Question 11: In each case, lifting or pushing, why must you exert a force to move the object?
Question 12: How much more effort does it take to lift or push two books instead of one?
5. Lift a book with your hands at a slow, constant speed from the floor to a height of about 1 m.
Repeat, this time lifting the book a distance of 2 m.
6. Push a book 1 m along the floor at a constant speed. Repeat, this time pushing the book a
distance of 2 m.
Question 13: How much more effort does it take to lift or push an object twice the distance?
Question 14: If work were defined as “effort,” how would you say work depends on the force
applied and on the distance moved?
Slide 4
Activity 1-1: Eﬀort and Work—Calculating Work
In physics, work is not simply effort. In fact, the physicist’s definition of work is precise and
mathematical. To have a full understanding of how work is defined in physics, we need to consider its
definition for a very simple situation and then enrich it later to include more realistic situations.
NOTE: All of the definitions of work in this unit apply only to very simple objects that can be idealized
as point masses or are essentially rigid objects that don’t deform appreciably when acted on by a force.
The reason for limiting the definition to such objects is to avoid considering forces that cause the
shape of an object to change or cause it to spin instead of changing the velocity or position of its
center of mass.
If a rigid object or point mass experiences a constant force along the same line as its motion, the work
done by that force is defined as the product of the force and the displacement of the center of mass of
the object. Thus, in this simple situation where the force and displacement lie along the same line
W = FxΔx
where W represents the work done by the force, Fx is the force, and Δx is the displacement of the center
of mass of the object along the x axis. Note that if the force and displacement (direction of motion) are in
the same direction (i.e., both positive or both negative), the work done by the force is positive. On the
other hand, a force acting in a direction opposite to displacement does negative work. For example, an
opposing force that is acting to slow down a moving object is doing negative work.
Question 15: Does this definition of work agree with the amount of effort you had to expend when you
moved books under different conditions? Explain.
Question 16: Does effort necessarily result in physical work? Suppose two people are in an evenly
matched tug of war. They are obviously expending effort to pull on the rope, but according to the
definition are they doing any physical work as defined above? Explain.
Slide 5
Force (200 Hz) Remote 1
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Activity 1-2A: Calculating Work When the Force and Displacement Lie Along the
Same Line
In this activity, you will use the IOLab to measure the force needed to pull the IOLab, on its wheels, up
the inclined smooth board (or other level surface). You will examine two situations. First you will exert a
force parallel to the surface of the ramp, and then you will exert a force at an angle to the ramp. You will
then be able to see how to calculate the work when the force and displacement are not in the same
direction in such a way that the result makes physical sense.
1. Set up the IOLab and ramp as shown in the diagram below. Attach a short string (about 50
cm) to the eyebolt screwed into the force sensor of the IOLab. Put one of the books or a block
on the IOLab. Taping the book or another object about the mass of the IOLab over the single
wheel will prevent the IOLab from flipping over. Support one end of the ramp so that it is
inclined to an angle of about 15–20°. Use the protractor or calculate to make sure you have an
angle of at least 15°.
Reminder: It is important to zero the Force Sensor on the IOLab with nothing pushing or
pulling on the eyebolt just before making measurements, so not on the ramp.
2. Find the force needed to pull the IOLab and book up the ramp at a constant velocity. Begin
graphing force and the displacement (position) as functions of time as you pull the IOLab and
book up the ramp slowly at a constant velocity. Pull the IOLab so that the string is always
parallel to the ramp. Pull the IOLab and book a measured distance along the ramp, say 0.5 m.
3. Use a time interval over which the force is relatively constant and record the average force
and the displacement. Using the software, find the average (mean) force applied to the IOLab
and book during the time interval when the IOLab was moving with a constant velocity. Make
sure it was really moving at nearly a constant velocity. Do not include the force to get the cart
moving.
Average force in the y direction pulling parallel to surface:
Slide 6
Force (200 Hz) Remote 1
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Activity 1-2B: Calculating Work When the Force and Displacement Lie Along
Diﬀerent Directions
Prediction 12: Suppose that the force is not exerted along the line of motion but is in some other
direction. If you try to pull the IOLab up along the same ramp in the same way as before (again with a
constant velocity), only this time with a force that is not parallel to the surface of the ramp, will the force
sensor measure the same force, a larger force, or a smaller force? Note that, the force sensor measures
the force only in the ydirection.
Now test your prediction by measuring the force needed to pull the cart and mass up along the ramp at
a constant velocity, pulling at an angle of 45° to the surface of the ramp. To prevent the IOLab from
flipping over backwards, be sure that the book is taped centered to the front of the IOLab, over the
single wheel.
1. Attach the string to the eyebolt as before. Measure the 45° angle with a protractor. Begin
graphing the force and the velocity and position as you pull the IOLab up at a slow constant
speed. Be sure the IOLab does not lift off the surface of the ramp.
2. Use a time interval over which the force is relatively constant and record the average force
and the displacement (position). Using the software, find the average (mean) force applied to
the IOLab and book during the time interval when the IOLab was moving with a constant
velocity. Make sure it was really moving at nearly a constant velocity. Do not include the force
to get the cart moving.
Average force component in the y direction when pulling at 45° to surface:
Question 17: Did it seem to take more “effort” to move the IOLab and mass when the force
was inclined at an angle to the ramp’s surface? Do you think that more physical work was
done to move the IOLab and mass over the same distance at the same slow constant speed?
Slide 7
Activity 1-2B: Calculating Work When the Force and Displacement Lie Along
Diﬀerent Directions
It is the force component parallel to the displacement that is included in the calculation of work. Thus,
when the force and displacement are not parallel, the work is calculated by
Question 18: Do your observations support this equation as a reasonable way to calculate the work?
Explain.
Question 19: Based on all of your observations in this investigation, was your choice in Prediction 11
the best one? In other words, did you pick the job requiring the least physical work? Explain.
Sometimes more than just the total physical work done is of interest. Often what is more important is
the rate at which physical work is done. Average power, < P >, is defined as the ratio of the amount of
work done, ΔW, to the time interval, Δt, in which it is done, so that
If work is measured in joules and time in seconds, then the fundamental unit of power is the
joule/second, and one joule/second is defined as one watt.
A more traditional unit of power is the horsepower, which originally represented the rate at which a
typical work horse could do physical work. We now define the equivalency between one horsepower and
watts as follows:
Slide 8
INVESTIGATION 2: WORK DONE BY CONSTANT AND
NONCONSTANT FORCES
Many forces in nature are not constant. A good example is the force exerted by a spring as you stretch
it. In this investigation you will see how to calculate work and power when a nonconstant force acts on
an object.
You will start by looking at a somewhat different way of calculating the work done by a constant force by
using the area under a graph of force vs. position. It turns out that, unlike the equations we have written
down so far, which are only valid for constant forces, the method of finding the area under the graph will
work for both constant and changing forces.
IOLab with force sensor calibrated
smooth board or other level surface at least 0.5 m long
meter stick or measuring tape
spring, unstretched length about 7 cm
Slide 9
Force (200 Hz) Remote 1
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Wheel - Position (100 Hz) Remote 1
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Wheel - Velocity (100 Hz) Remote 1
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Activity 2-1: Work Done by a Constant Lifting Force
In this activity you will measure the work done when you lift an object from the floor through a measured
distance. You will use the force sensor to measure the force and the wheel to measure distance.
1. Set up the ramp as shown in the picture to the right; it will be almost vertical against the wall
or table. Roll the IOLab along the ramp positioned almost vertically such that the wheels stay
in contact with the ramp.
2. Practice lifting the IOLab by the string which is attached to the eyebolt screwed into the force
sensor.
3. Click record with the IOLab resting on the ground, now lift the IOLab at a slow, constant
speed through a distance of about 0.5 m. When you have a set of graphs in which the IOLab
was moving at a reasonably constant speed, answer the following.
Question 21: Did the force needed to move the mass depend on how high it was off the floor,
or was it reasonably constant?
Depends on height
Does not depend on height
4. Use the analysis features of the software to find the average (mean) force over the distance
the mass was lifted. Record this force and distance below.
Average force:
Distance lifted:
5. Calculate the work done in lifting the mass. show your calculation.
Work done:
Slide 10
Force (200 Hz) Remote 1
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Activity 2-1: Work Done by a Constant Lifting Force
6. Plot Force vs Wheel (ry). This called the “Parametric plot mode”, indicated by the button
.
Clickanddrag the data below the “Force vs. Wheel plot” to plot those parts of the two
quantities that are relevant.
7. Notice that force times distance is also the area of the rectangle under the force vs. position
graph. One can find the area under the curve by counting squares for instance. In some
cases, as we saw before, it can be calculated without resorting to counting unit squares.
Comment: This activity has dealt with the constant force required to lift an object against the
gravitational force at a constant speed. The area under the force vs. position curve always
gives the correct value for work, even when the force is not constant. (If you have studied
calculus you may have noticed that the method of calculating the work by finding the area
under the force vs. position graph is the same as integrating the force with respect to
position.)
Slide 11
Force (200 Hz) Remote 1
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Wheel - Position (100 Hz) Remote 1
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Activity 2-2: Work Done by a Nonconstant Spring Force
In this extension you will measure the work done when you stretch a spring through a measured
distance. First you will collect data for the force applied by a stretched spring vs. distance the spring is
stretched, and you will plot a graph of force vs. distance. Then, as in Activity 21, you will be able to
calculate the work done by finding the area under this graph.
1. Set up the ramp, IOLab, and spring as shown in the diagram. The spring is attached to the
board by the binder clip. The ramp or table should be horizontal.
Comment: We assume that the force measured by the force sensor is the same as the force
applied by the cart to the end of the spring. This is a consequence of Newton’s third law.
2. Rezero the force sensor with nothing pushing or pulling on it.
3. Begin graphing force and position as the IOLab is moved such that the spring gradually
stretches from its equilibrium length (with no force pulling on its end), y=0.0 to y=0.2 m.
4. Then, as before, do a parametric plot of force vs. position. When the spring is unstretched,
the force should read zero.
5. Calculate the spring constant from the graph above, the slope of force as a function of
position using a calculator.
Spring constant (k):
Question 23: Compare this force vs. position graph to the one you got lifting the mass in
Activity 21. Is the spring force a constant force? Describe any changes in the force as the
spring is stretched.
Question 24A: Can you use the equation W = FxΔx for calculating the work done by a non
constant force like that produced by a spring?
Yes
No
Question 24B: Explain.
6. Calculate the work done in stretching the spring using the area.
Area under force vs. position graph:
Slide 12
INVESTIGATION 3: KINETIC ENERGY AND THE WORK–
ENERGY PRINCIPLE
Investigation 3 will begin with an exploration of the definition of kinetic energy. Later, we will return to
the method of the previous slides of measuring the area under the force vs. position graph to find the
work, and we will compare the work done to changes in the kinetic energy.
What happens when you apply an external force to an object that is free to move and has no frictional
forces on it? According to Newton’s second law, it should experience an acceleration and end up
moving with a different velocity. Can we relate the change in velocity of the object to the amount of work
that is done on it?
Consider a fairly simple situation. Suppose an object is lifted through a distance and then allowed to fall
near the surface of the Earth. During the time it is falling it will experience a constant force as a result of
the attraction between the Earth and the object—the gravitational force. You discovered how to find the
work done by this force in Investigations 1 and 2. It is useful to define a new quantity called kinetic
energy. You will see that as the object falls, its kinetic energy increases as a result of the work done by
the gravitational force, and that, in fact, it increases by an amount exactly equal to the work done.
First you need to find a reasonable definition for the kinetic energy. You will need the following:
two thick books
Slide 13
Activity 3-1: Kinetic Energy
In this activity you will explore the meaning of kinetic energy, and see how it is calculated.
1. Toss one book up in the air and catch it. If you throw it faster it will go higher. Alternate
between fast tosses and slow tosses. Notice how much effort it takes to throw it and to catch
(stop) it when it is moving quickly or slowly.
Question 31: Does the effort needed to stop the book seem to change as its speed
increases? How does it change? Explain.
Question 32: Does the effort needed to throw the book seem to change as its speed
increases? How does it change? Explain.
2. Now toss the two books together (some rubber bands will help in having them stay together).
Compare tosses of one and two books that go up at the same speed. Again notice how much
effort it takes to toss and stop the book(s).
Question 33: Does the effort needed to stop the two books seem to change as the mass
increases compared to a single book? How does it change? Explain.
Question 34: Does the effort needed to throw the two books seem to change as the mass
increases compared to a single book? How does it change? Explain.
Comment: When an object moves, it possesses a form of energy because of the work that was done to
start it moving. This energy is called kinetic energy. You should have discovered that the amount of
kinetic energy increases with both mass and speed. In fact, the kinetic energy is defined as being
proportional to the mass and the square of the speed. The mathematical formula is K=1/2 m v2 The unit
of kinetic energy is the joule (J), the same as the unit of work.
Slide 14
rᵧ (m)
Wheel - Position (100 Hz) Remote 1
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Activity 3-2: Your Kinetic Energy
In this activity you will examine how you can graph the kinetic energy of an object such as your body in
real time. You will need the following:
IOLab
a string about 2m long
1. To calculate kinetic energy you will need to know your mass in kilograms. Use the fact that
1.0 kg weighs 2.2 lb on Earth to find your mass in kilograms.
Your mass:
2. Attach the string to one end of the IOLab. You are ready to record your velocity as you walk
your IOLab – like a dog. Begin graphing while walking away from the computer slowly, then
more quickly, and then stop. Now, carefully so the IOLab does not turn around, walk slowly
back toward the computer.
Question 35: Now calculate your kinetic energy at several instances while moving away from
your computer and when you are moving back to the computer using your mass and the
velocity recorded by the IOLab. Is it possible to have negative kinetic energy? Explain.
Question 36A: Which would have a greater effect on the kinetic energy—doubling your
velocity or doubling your mass?
double the mass
Question 36B: Explain
double the velocity
they have the same
effect
Slide 15
Activity 3-2: Your Kinetic Energy
When you apply a force to an object in the absence of friction, the object always accelerates. The force
does work and the kinetic energy of the object increases. Clearly, there is some relationship between the
work done on the object and the change in its kinetic energy.
Prediction 31: What do you think is the relationship between work done and change in kinetic energy of
an object? Explain.
In the next activity, you will examine this relationship, called the work–energy principle, by doing work
on the IOLab with a spring.
Slide 16
Force (200 Hz) Remote 1
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Activity 3-3: Work–Energy Principle
1. Measure the weight of the IOLab by hanging it from the eye bolt. Calculate the mass of the
IOLab from the weight. Make sure you rezero the force sensor with no force applied prior to
weighing the IOLab. show your calculations below.
Mass of IOLab:
2. Set up the IOLab and spring as shown in the diagram in Activity 22 (slide 11).
3. Begin recording, and then pull the IOLab along the board so that the spring is stretched about
20 cm from the unstretched position. Release the IOLab, allowing the spring to pull it back at
least to the unstretched position.
What is the time you released the IOLab?
What is the IOLab's velocity at that time?
What is the time at which the IOLab reached the “zero” position?
What was its velocity when it reached the “zero” position?
4. Change to the force vs position graph using the “Parametric plot mode":
. Clickanddrag
the data below the “Force vs. Wheel plot” to plot those parts of the two quantities that are
relevant.
5. Calculate the value of the work done by the spring by calculating the area under the curve of
the force vs position graph. The position should go from 20 cm to zero. The force will go from
its maximum to zero as well, so make sure you zoom in on the right part of the graph. The
data gets more difficult to interpret when the spring is fully retracted. show your calculation.
Work done by spring:
6. Calculate the change in kinetic energy of the IOLab using its mass and the velocity when the
force becomes zero.
Change in kinetic energy:
Question 37: How does the work done on the cart by the spring compare to its change in
kinetic energy? Does this agree with your prediction? Is there a loss due to friction? How
much?
Question 38: State the work–energy principle that relates work to kinetic energy change in
words for the IOLab and spring system that you have just examined.

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