Download ENERGY and WORK - Rutgers Physics

ENERGY and WORK
Purpose:
 To understand work, potential energy, & kinetic energy.
 To understand conservation of energy and how energy is converted from one form
to the other.
Apparatus: Pasco track, Pasco cart, LabPro interface and cables, motion sensor,
pulley, mass bucket & long thin string, assorted mass hanger weights
Background: Reread your textbook to refresh your memory on the concepts of energy,
work, kinetic energy, and potential energy. In this lab we will be using four equations,
which we summarize here:
W = Fx cos ,
(work)
(1)
where  is the angle between the force F doing the work and the displacement x of the
object during the time work is being done. The kinetic energy of a mass M moving with
speed v is:
KE = ½ M v2
(kinetic energy)
(2)
The gravitational potential energy of a mass M raised a distance y above the zero level
of potential energy is:
Energy -- 1
PE = Mgy
(gravitational potential energy)
(3)
The point where the potential energy is zero can be arbitrarily chosen (since only changes
in potential energy can be measured). It is conventional to make the lowest point in
height the zero. Conservation of energy states that:
KEi + PEi + Wnc = KEf + PEf ,
(energy conservation)
(4)
where Wnc is the work done on the system by non-conservative forces such as friction.
Work done by conservative forces like gravity is taken care of by defining the potential
energy due to the force. Note in the case of friction that the force of friction always
opposes the motion ( = 180o) so that Wnc is always negative. Friction always removes
energy from the system. Also remember that work is a process that transfers energy into
or out of a system. Although a system can contain energy, it cannot contain work. [The
relation between work and energy is similar to that of learning and knowledge. You can
have more or less knowledge, but you do not have learning. You gain knowledge by
learning.]
For the ActivPhysics exercises you will also need the potential energy of a spring when
compressed a distance x,
PE = ½ k x2,
(potential energy of a spring)
(5)
where k is the force constant of the spring (F = - k x). Note that the potential energy is
zero when the spring in not compressed.
Experimental Set-up: You will study a large wheeled cart of mass M (~ 0.2 - 0.5 kg) on
a horizontal low friction track. M is attached to a smaller mass m (~ 0.005-0.015 kg) by
means of a string passing over a pulley. m is allowed to fall vertically to the floor through
a distance y. The initial speed of both m and M are vi = 0; they are released from rest.
You will measure vf, the final speed of M, after the small mass m travels a distance y.
How are the speeds of m and M related?
You will use the same sonic motion sensor as you did in the first two labs. Open
WorkEnergy.xmbl. file. The velocity at any time or position can be obtained from the
Logger Pro program.
The speed vf can depend on three variables -- M, m, and y -- that you can vary to test the
conservation of energy and examine whether any discrepancy can reasonably be
attributed to friction.
Important checks:

Check that the low friction track is level.
Energy -- 2


Be sure to add the mass of the bucket (written on the bucket) to the small masses
you put inside to get to the total m.
Because of friction, there is a minimum value for m that is needed to produce any
acceleration. Determine this value and be sure that you use considerably larger
values of m for your experiment. Otherwise the friction will dominate and give poor
agreement.
Activity 1 (80 min): Dependence of vf on m and y and their product.
Use the set-up described above to determine the final speed of the cart for several
different values for m while keeping M constant. In each case choose the height y
above the floor at which m is released so that the product my is a constant. Then make
additional measurements for the case where only y varies. Answer the questions on the
lab hand-in sheet.
Activity 2 (40 min): Relationship between kinetic energy and total
potential energy. Using the data from Activity 1 for which m is a constant, make a
plot of total potential energy versus vf and fit the data to curves that vary as vf, vf2, and vf3
to see which gives the best fit. Answer the questions on the lab hand-in sheet.
Activity 3 (30 min): Conservation of energy. Use your data from Activity 1 to
determine whether conservation of energy holds. Discuss any discrepancies as indicated
on the lab hand-in sheet.
Activity 4 (30 min): Work. Draw free-body diagrams for m and M for the
experimental set-up used above. Calculate the work each of these forces does during the
time m falls to the floor. Include friction. Use symbols rather than numbers and be
ENERGY and WORK
careful about the signs.
Name: __________________________________________________ Section: ________
Preliminary Questions
1. A 130 g arrow is shot straight up with an initial velocity of 20 meters/second.
a) What is its initial kinetic energy? To what height does it go?
b) At what height does the arrow have maximum potential energy? What is its maximum
potential energy?
Energy -- 3
c) At what height does the kinetic energy equal the potential energy?
d) How much work does gravity do on the arrow between the time it is shot and when it
reaches its peak height? Between when it is shot and returns to the ground?
ENERGY and WORK
Name: ____________________________________________ Section: ______________
Partner: ___________________________________________ Date: _______________
Partner: ___________________________________________
Activity 1 (60 min): Dependence of speed vf on m and y and their product.
Determine the final speed (before hitting the floor) for several different values for m
while keeping M constant. In each case choose the height y above the floor at which m
is released so that the product my is a constant. To improve your accuracy repeat the
measurement three times for each case and record the average speed and acceleration for
the elapsed time t. Use values of y between 0.2 and 0.8m.
M
m
y
Table 1
PEm
my
average t
vi
vf
m
[PE is the initial gravitational potential energy of m given by Eq. (3).]
Energy -- 4
Now repeat the experiment with the same fixed values for M and m as in the first line
m
of data in Table 1 but with different values of y so that PE is not a constant.
M
Table 2 (both M and m constant)
PEm
y
my
average t
m
vi
vf
What can you conclude from your data in Tables 1 and 2 about the relationship between
f
m
v and m, y, and PE ? How do your data lead you to these conclusions? [Be precise;
don’t draw conclusions not supported by the data.]
Activity 2 (30 min): Relationship between kinetic energy and total potential energy.
In Tables 1 and 2 you calculated PEm. Where did you choose the zero of potential energy
to be?
You now want to calculate the total potential energy of m and M. Do you have to choose
the zero to be at the same place for both masses? Explain.
Fill in the following table using all your data, which have the same value for m (Table 2
and the first line of data in Table 1). Should you include y = 0 as a data point?
Table 3
M
m
PEm
PEM
PEM+m
vf
y
Using Graphical Analysis, make a plot of PEm+M versus vf for the data given in Table 3.
Make a fit to the data of a straight line (PEm+M  vf), a quadratic curve (PEm+M  vf2) and
Energy -- 5
a cubic curve (PEm+M  vf3). For each fit record the value of R2. If a printer is available
make a copy of your graph showing all three fits and attach it to your report. [Pay
attention to the appearance and quality of the graph.]
Which curve provides a better fit to you data? How do you know it’s better?
Explain why these data strongly suggest that the initial potential energy is related to the
final kinetic energy.
We have considered only the initial potential energy and the final kinetic energy. Why
could we ignore the final potential energy and the initial kinetic energy?
Activity 3 (20 min): Conservation of energy. Use your data from Table 1 to determine
whether conservation of energy holds. Use that data to fill in the following table:
Table 4
Initial K.E. of M
Initial K.E. of m
Initial P.E. of M
Initial P.E. of m
Total initial energy of m + M
Final K.E. of M
Final K.E. of m
Final P.E. of M
Final P.E. of m
Total final energy of m + M
Difference between initial and final total energies
From this table what can you conclude about energy during the fall?
You did this experiment to verify that energy is conserved, but your data show a
discrepancy between the initial and final total energies. To what do you attribute this
discrepancy?
Energy -- 6
Your partner argues that there are actually three possible sources of the discrepancy -friction, random error, or the track is not level. Describe additional experiments or tests
you could do to find whether each of these explanations of the discrepancy is a possible
source:
Random error:
Track not level: [Can you estimate the difference in height of the track must be between
where the cart starts and it ends in order to produce the size discrepancy you observed?
Which end must have been higher?]
Friction: [How can you measure the force of friction acting on the cart? Can you
demonstrate that friction is acting without actually measuring it?]
Activity 4 (20 min): Work. Draw free-body diagrams for m and M for the experimental
set-up used above. Calculate the work each of these forces does during the time m falls
to the floor. Include friction. Use symbols rather than numbers and be careful about the
signs.
What is the total work done on M during the fall?
What is the total work done on m during the fall?
What is the total work done on M+ m during the fall?
Energy -- 7
What is wrong with this statement? During the time that m falls through y the force of
f
f
f
friction F removes an amount of work W = -y F from the system of M + m.
Energy -- 8