Download Lab Exercise 7

ETSU Physics and Astronomy
Technical Physics Lab – Exp 7 – Page 44
Experiment 7. Conservation of Energy
As we have discussed in lecture, the Law of Conservation of Energy is a very powerful
experimentally-based principle which we can use to analyze changes in physical systems. We
have also learned that energy can take many forms, two of which, mechanical energy, Emec ,
and thermal energy, Eth , will be the focus of this experiment.
We will be working with a 4 meter air track. The air track is a laboratory device for producing
almost frictionless linear motion over a distance of more that 3 meters. The motion of
“gliders”, special light aluminum forms that move on a cushion of air only hundredths of a
millimeter thick, is observed. The track over which the glider moves is a perforated tube of
triangular cross section; air is pumped into the tube at one end and exits upwards through
many tiny holes along the upper two surfaces of the track. Ideally, the air uniformly supports
the glider so that it is free to move on the track with very little friction.
In this lab session, we will first estimate the work done by friction as the glider slides along
the air track. We will then examine a collision of the air track glider with the relatively
motionless end of the air track. The bumpers attached to the air track and the glider
provide for a nearly elastic collision. Finally we will verify conservation of energy by tilting
the air track, so that the conservative force of gravity as well as the nonconservative force of
friction is acting.
Because we have only one air track, much of this procedure will take the form of a demonstration, involving the instructor and whatever students are needed to perform the measurements. It is very important, however, for all students to be actively involved in observing
the experiments. A sound knowledge of the experiments and the relevant measurements will
be needed to complete your lab reports.
Procedure
In addition to the air track and air track glider, we will be making extensive use of photogates
to provide precise measurements of time. As we have already seen in earlier experiments,
the photogate can provide a precise measurement of the time during which its infrared beam
is interrupted. As you will see, there is a card attached to the air track glider which has
a known length. By combining this known length with the time it takes for the card to
pass through the beam, we can estimate the instantaneous velocity of the air track glider.
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Technical Physics Lab – Exp 7 – Page 45
Because we also will make a precise measurement of the mass of the glider, we will also be
able to calculate the kinetic energy of the glider.
1. Measuring change in thermal energy due to friction
We can consider the glider, air track, earth system to be a closed system, so that
∆Emec + ∆Eth = 0
where ∆Eth is related to the magnitude of the kinetic friction force fk and the displacement
d by ∆Eth = fk d. If the air track were completely level, there would be no change in vertical
position as the glider slides along the track, because there is no change in the gravitational
potential energy. In that case we can write
∆K + fk d = 0
and use the measured change in kinetic energy to calculate the change in thermal energy
and thus the magnitude of the work done by friction. Because the air track is so close to
frictionless, however, if the air track is even slightly tilted, there may be a slight change in
height ∆ǫy , and this change in gravitational potential energy may affect our calculations.
There is a remedy for this. If we start the glider from one end (trial 1), conservation of
energy implies
1 2
1 2
mvf,1 − mvi,1
+ mg∆ǫy + fk d = 0
2
2
where m ≡ mass of glider, and vi,1 and vf,1 are the initial and final speeds of the glider. If
we then start the glider from the other end (trial 2), we can write
1 2
1 2
mvf,2 − mvi,2
− mg∆ǫy + fk d = 0
2
2
Note that the term for gravitational potential energy has changed sign, since the vertical
displacement is in the opposite direction. If we add the two equations we now have an
equation to solve for fk d:
1 2
1 2
1 2
1 2
− mvi,1
) + ( mvf,2
− mvi,2
) + 2fk d = 0
( mvf,1
2
2
2
2
The measurements needed to get the initial and final velocities consist of time intervals. The
width of the card attached to the glider which blocks the photogate light beam is Lcard , and
we will measure this. We divide Lcard by the time interval that the card blocks the light
beam to get an approximate instantaneous velocity (for example, vi,a = Lcard /ti,a ). We will
measure approximate instantaneous velocities at the 50.0 cm and 350. cm positions on the
air track glider for trial 1, and at the 45.0 cm and 345. cm positions for trial 2. In both cases,
the photogates are at the 47.5 cm and 347.5 points. Explain why this is so. This means
that the magnitude of the displacement over which the kinetic friction works is d = 300. cm.
You will thus need to keep track of time intervals associated with the glider passing through
the photogates. We will repeat each step of the experiment 3 times. It will be helpful to
tabulate the results. One such table might look like the following:
Technical Physics Lab – Exp 7 – Page 46
ETSU Physics and Astronomy
Experimental Data For Part 1 of Exp. 7
Trial
1
ti,a
ti,b
ti,c
vi,a
vi,b
vi,c
1
tf,a
tf,b
tf,c
vf,a
vf,b
vf,c
2
ti,a
ti,b
ti,c
vi,a
vi,b
vi,c
2
tf,a
tf,b
tf,c
vf,a
vf,b
vf,c
You can then calculate ∆Eth,a , ∆Eth,b , and ∆Eth,c and average the results. What is the
change in thermal energy due to kinetic friction? Assuming the friction is constant along the
air track, what is the magnitude of the kinetic friction? Calculate the coefficient of kinetic
friction. You will need the mass of the glider for this. See the procedure notes. You may
assume that the gravitational acceleration g = 9.80 m/s2 .
2. Examining A Glider-Immovable Target Collision
Having determined the change in thermal energy associated with friction on the air track
glider, we can now examine the nature of a collision of the glider with the end of the track.
We assume that the air track is immobile. If that is the case, an elastic collision with the
end of the track should leave the kinetic energy of the glider unchanged. We will launch
the glider toward the end of the track, recording its velocity before and after the collision.
As before, we will use the measurement of time intervals and the known length of the card
attached to the glider to calculate the initial and final velocities. We will make 3 trials with
varying initial velocities (and so final velocities). In each case we will calculate the fraction
f = Kf /Ki where Ki and Kf are the initial and final kinetic energies, respectively. Once
again, it would be useful to tabulate your data. Here, you can construct your own table.
What is the average fraction f for the 3 trials? An ideal elastic collision would have f = 1
Do you believe thermal energy loss due to friction is a significant source of loss of kinetic
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Technical Physics Lab – Exp 7 – Page 47
energy? Why?
3. Gravitational Potential Energy
Our final experiment introduces a change in gravitational potential energy by tilting the air
track. We will remove a cylinder from 1 end of the track support so that the air track is at
an angle. If the cylinder has height h, and the distance between the supports is L, the track
makes an angle θ = tan−1 (h/L). Once this is measured, the change in height ∆y is given by
the distance d along the track travelled by the glider multiplied by sin θ. See below.
Now, we will make 3 trials in which we release the air track glider from rest from the same
point (the 20.0 cm point) and measure the velocity v at the 320.0 cm point. In that case
∆K will just be 21 mv 2 . We will use the energy conservation equation,
∆K + mg∆y exp + fk d = 0,
and our measurements to solve for ∆y exp for each individual trial. Remember that we know
fk from the first procedure. Again, it will be useful to tabulate your data. Here, you can
construct your own table. Average the 3 individual trials and compare the absolute value
of the result to ∆y = d sin θ. What is the percent difference between the values? What are
some possible sources of error?
Procedure Notes
You will need to measure and record several experimental quantities. These include:
1) The mass of the glider, Mglider =
2) The length of the card attached to the glider, Lcard =
3) The height h of the cylinder in part 3 h =
4) The length L between supports of the air track in part 3 L =
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Technical Physics Lab – Exp 7 – Page 48
Many quantities are not given in SI units; you will need to convert them to the proper SI
units. Recall 100 cm = 1 m, and 1000 g = 1 kg.
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Technical Physics Lab – Exp 7 – Page 49
Measuring Apparatus
We will discuss the apparatus used in the experiment in detail at the beginning of the session.