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Introduction
This experiment examines the energy and momentum of carts on an
air track before and
after collisions. The air track is used to reduce friction to a
very low value. Timers
measure the speeds of the carts. A mass balance measures the
masses of the carts. You
should study the concepts of momentum, conservation of momentum,
kinetic energy, and
elastic and non-elastic collisions for this lab.
You will do three experiments. The first will examine the
residual effects of friction, the
second will look at an elastic collision, and the third an
inelastic collision.
Apparatus
2 meter air track,
air track glider,
photogate timer system,
mass balance.
The picture above shows detail of the timer
control and read out
The left picture shows a glider with its flag on the air track.
The timer photogate is in the
U-shaped black bridge and the timer controls and readout are in
the black box.
Figure 1. Apparatus for Collision Experiments.
glider 1 glider 2
timer 1 timer 2
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General Setup
1. First make sure the track is level. When it is level a cart
will not accelerate in eitherdirection. There are leveling screws
underneath one end of the track. This technique is
very sensitive. Can you detect if your track is not completely
straight?
2. Attach a rubber bumper and a flag to each glider. The flag
triggers the photogate. Get afeel for the low friction environment
by playing with the gliders and watching
collisions. Try out both the rubber bumpers and the pin/wax
attachments that make
the carts stick together.
3. For experiments A and B you will measure the speed of the
cart by measuring thetime interval for the flag on the cart to pass
through the photogate. Measure the length
of the flag.
4. For each experiment you should play around with the
positioning of the gliders beforetaking data. Practice recording
the time intervals as the carts pass through the timers.
5. You should record two good trials in each procedure. Tabulate
your data. Note thecart masses at the start of each experiment and
tabulate the times for each individual
run. Leave columns where you can fill in the momentum and energy
for each glider
before and after the collision and for total momentum and energy
before and after the
collision. You may find the table needs a double page but it
will allow you to compare
momenta and energies immediately.
Review the properties of elastic and inelastic collisions.
Remember that all collisions
conserve momentum, and that elastic collisions are a special
type that also conserve
energy, i.e. no energy is lost to deformation or changes in
internal energy of the colliding
objects. Although this sounds unlikely to happen in everyday
life (do people ever collide
elastically?) elastic collisions are very important for atomic
and nuclear phenomena. (Do
air molecules collide elastically?)
Pre-lab Homework:
1. Do cars colliding at freeway speeds collide elastically or
not? If not, what happensto the energy lost? Car manufacturers now
make 5 mph bumpers. What do you
think this means? Would it be possible to make 50 mph bumpers?
If it could be
done would it be a good idea?
2. The mass m2 is initially at rest in the following.a) For an
elastic collision with m1 = m2, and m1 moving at speed vo, what
is
the speed of each mass after the collision in terms of vo?
b) For an elastic collision with m1 = 3 m2, the final velocity,
v2, was found tobe equal to 1.5 vo. Find the final velocity v1 in
terms of vo.
c) For an elastic collision with m1 = m2/2, the final velocity,
v1, was found tobe equal to -0.33vo. Find the final velocity,
v2.
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Pre-lab Homework
3. Home Experiments.
Hint: Remember that momentum, like velocity, is a vector.
a) Take a small bouncy ball and throw it at a solid wall. Catch
it when it comes back to you.
What is its momentum before the bounce? What is its momentum
after the bounce? How can
momentum be conserved here?
b) Take a small ball and a large ball (a tennis ball and a
basketball, or a ping-pong ball and a tennis ball) and drop them
to
the floor together so that the small ball is just above the
large ball
as they fall. Describe what happens when the small ball
rebounds
off the large ball. Does this behavior violate Conservation
of
Momentum? Why or why not? Explain qualitatively (and
quantitatively if you can) why the small ball bounces higher off
the
large ball than if the floor when dropped alone. How would youdo
a similar experiment with the air track and the gliders?
Experiment A: Does the air track eliminate friction?
Use just one glider and start it close to one end of the track.
Put the photogates about one
third and two thirds of the distance down the track. Give the
glider a gentle push and
measure the times for the glider to pass each photogate. From
this calculate the speed as
the glider passes each photogate. Does the glider lose or gain
speed? Start the glider at the
other end and repeat the exercise. Note speed gain or loss for
each experiment and explainthe data. Is the track level? (If you
decide no then re-level it) Are any effects from
friction measurable?
Experiment B: An inelastic collision
Pre-lab Homework:
4. Suppose a 100 g mass moving at 2 m/s collides with another
100 g mass initially
at rest. The two masses stick together. What is the final speed?
How much energy is
lost? Express the energy lost as a percentage of the initial
energy.
B1. Use two un-weighted gliders.
B2. If necessary replace the rubber bumpers with a pin on one
glider and a wax-filled
receptacle on the other glider. The two gliders should stick
together on collision.
Check this. Remove the flag from one of the gliders. This is the
glider that will
initially be stationary (#2). Measure the glider masses as you
will use them (i.e. with
whatever pins/wax/flags etc attached).
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B3. Put glider #2 at rest between the photogates and push glider
#1 gently from the end
of the track towards it. Measure the passage times for glider #1
before collision and
the two gliders after collision. Reset the timer before the
start of each measurement.
B4. Do a few trial runs, watching each glider closely to be sure
your data really
represents the speeds before and after the collision.
B5. After making preliminary trials, make two good measurements
of the times. Calculate
speeds and momenta.
B6. Compare initial and final momenta and energies. What
fraction of the energy is lost?
What fraction of energy would you expect to be lost? Is the
momentum conserved?
What happened to the energy lost in the collision? Can it be
recovered?
Experiment C: An elastic collision with m2 > m1
By using rubber bumpers on the gliders you should be able to
make them bounce off each
other with little loss of energy. In this experiment you will be
able to compare the
momentum before and after the collision and the energy before
and after the collision. If
the rubber bumpers are not perfectly elastic, predict what you
should expect as you
compare initial and final momenta and energies.
You should start with one of the gliders (#2) at rest and the
other (glider #1) moving
towards it. t0 is the time glider #1 takes to pass through the
photogate before the collision.
t 1 and t 2 are the times gliders #1 and #2 take to pass through
the photogates after
collision. We will refer to the initial speed of glider #1 as
v0, and the final speeds of gliders
1 & 2 as v1, and v2 respectively. For glider #1 you will
need to measure two transit times
on a single photogate. To do this use the timer in the gate mode
with memory on. Reset
the timer before the start. The displayed time is t 0, The
memory contains the sum of thefirst and second times measured. So t
1 can be calculated by subtracting the displayed time
from the time in memory. Practice and convince yourself the
timer works as described.
C1. Take two gliders with rubber bumpers. Add extra mass to one
glider till it has about
double the mass of the other. Note the masses. Practice by
putting the heavy glider
at rest at the center of the track and push the second towards
it. What happens?
Compare your results to your homework question 2c.
C2. Place the photogates about 1 m apart on the level air track.
Do not worry about being
exact, the separation distance between photogates does not alter
the results.
C3. Place glider #2 in between the photogates and start the
other glider from the end. Usethe timer in the gate mode with
memory on. Reset the timer before the start of each
measurement.
C4. Do a few trial runs, watching each glider closely to be sure
your data really
represents the speeds before and after the collision.
C5. After making preliminary trials, make two good measurements
of the times. Calculate
speeds and momenta before and after the collision.
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C6. Compare initial and final momenta and energies. Are your
data good enough to be
able to tell if the gliders are perfectly elastic?
Experiment D: Newtons Cradle
Newtons Cradle (shown below) is often sold as an executive desk
toy.
Pull one of the masses aside and let it fall. Record what
happens. Why cant you have
two masses pop out on the other side with lower speeds? Try it
with 2 masses pulled to
one side and predict what will happen before you do it.
