Lab: Conservation of Momentum and Energy
Goal: The purpose of this experiment is to study the principle of conservation of momentum in collisions using
two bodies. We will also calculate the amount of kinetic energy lost in elastic and inelastic collisions.
Theory: When bodies collide with each other, the total momentum p = mv, is always conserved regardless of
the type of collision provided no external forces are present. There are two types of collisions. In an elastic
collision, both the kinetic energy and the momentum are conserved. An inelastic collision is one in which only
the momentum is conserved. Most collisions observed in nature are inelastic. A collision is completely inelastic
when the bodies stick together after a collision.
In this experiment, we will use two carts rolling on an Aluminum track to study two body collisions in one
dimension. Consider the situation shown in the figure below.
The conservation of momentum before and after the collisions can be written as follows:
Where, M1 and M2 are the mass of the carts, and
and
correspond to initial and final velocities.
If the collision is elastic, the conservation of kinetic energy implies that:
Materials: Carts, Mass bars, Aluminum track, two photogates, Aluminum flags, lab pro, logger pro
Procedure:
1. Level the track by setting the cart on the track to see which direction it rolls. Use the leveling feet at the end
of the track to raise or lower that end of the track. Measure the mass of the two carts. One is called the
Collision cart and the other is called the Dynamics cart.
2. First, do a few trails to observe the qualitative behavior as the carts collide elastically. Place the carts on the
track with the magnetic bumpers facing each other. The carts should repeal as they are brought close to each
other. (Push the plunger all the way in on the Collision cart so that it is out of the way.) Experiment with the
following situations and note your observations (Make sketches of your observations to include in your lab
report. Draw velocity vectors with approximate relative magnitudes and directions.)
i. Place one of the carts near the mid-point of the track. Push the second cart with an initial
velocity towards the stationary cart.
ii. Next, push the two carts towards each other with approximate the same speed.
iii. Push one cart with a slow velocity and a second one with a faster velocity so that it catches up
with the slower cart.
iv.
Place two mass bars on one of the carts, so that that cart weighs three times the other cart. First,
place the heavy cart at the center of the track and push the other cart with an initial velocity.
Next, place the lighter cart at the center and push the heavier cart with an initial velocity.
3. Next, we do a few trails to observe the qualitative behavior for a completely inelastic collision. Remove the
additional masses from the cart, and turn one of the carts around so that the magnetic bumpers are no longer
facing each other and the hook and pile ends are towards each other. Repeat the procedures listed in step 2
noting your observations in your lab book.
4. Now we will make quantitative observations by measuring the velocities before and after the collisions
using the photogate timers. Attach the two flags to the Dynamics cart and the Collision cart. Measure the
resulting masses of the cart. In Logger Pro go to “File”… “Open” … “Experiments” … “Probes & Sensors” …
“Photogates” … “Two Gate Timing”. When the file opens click “Connect” twice for the two photogates.
Enter the width of the flags on the screen under “Photogate Distance.”
5. Experiment with the photogates to get comfortable with how they work. Reset the photogate timers after each
trial. Make sure to keep track of which cart goes through which photogate first, second, third etc.
6. Now, we make quantitative measurements corresponding to elastic collisions. Place the Collision cart in the
middle of the track, and give the Dynamics cart an initial velocity so that it passes through the first photogate
timer and collides with the second cart. You will observe that after the collision, the second cart moves forward
and passes the second photogate. Calculate the velocities and change in momentum for each cart. Is the
momentum conserved? Calculate the relative error by calculating any possible change in momentum by the
total momentum before collision. Repeat for at least three different trials corresponding to different initial
speeds.
IMPORTANT: The collisions must occur after the cart has passed completely through the
photogate and after the collision, the carts must be fully separated before either cart interrupts a
photogate.
NOTE: Immediately after the final times are recorded, the carts must be stopped to prevent them
from triggering the photogate again due to rebounds.
7. Place mass bars on the two carts to change their total masses and measure the velocities before and after a
collision. Calculate the relative error in each case.
8. Next, make measurements corresponding to a completely inelastic collision. Measure the final velocities for
at least three different initial velocities. Also measure the velocities corresponding to equal and unequal masses
before and after collision. Is the momentum conserved?
9. Calculate the change in the kinetic energy before and after the collision for both elastic and inelastic
collisions. Is the kinetic energy conserved for any of the cases? What happens to the lost kinetic energy?
10. By using carts that roll, we have reduced friction a great deal but we have not eliminated it. Estimate the
loss of energy due to friction. You can do this by using the Collision cart and calculating its change in
momentum from the cart passing the first and second photogates. How does the percentage loss in error
compare to the relative error you calculated for the momentum and energy change for each collision?