Purpose: To observe the quantities that are conserved in straight line collisions where the objects recoil after the collision and where the objects stick together during the collision.
THEORY: In an elastic collision both kinetic energy and momentum are conserved. In the following equations; 1 and 2 designate the two objects colliding, unprimed variables indicates those before the collision and primed variables indicated after the collisions, p is momentum, KE is kinetic energy, M is mass, and V is velocity.
Conservation of momentum:
Conservation of kinetic energy:
Solving these two sets of equations for the velocities after the collision
If M1 = M2 them V1` = V2 and V2` = V1 .
If the second object had a velocity V2 = 0 before the collision the equations become
and
If the objects stick together after the collision the collision is a perfectly inelastic collision. In such a collision the velocities of the two objects after the collision are the same. Only momentum is conserved in the inelastic collision.
Conservation of momentum
Since V2 = 0 and V`1 = V`2 the above solved for the velocities after the collision becomes
Where the coefficient of restitution for a perfectly elastic collision is e = 1 and for a perfectly inelastic collision is e = 0. The equation for the velocities after the collision becomes
.These two equations give the same results as obtained for the elastic collision if e=1 and for the inelastic collision if e=0.
EQUIPMENT: Computer, and VideoPoint software.
PROCEDURE: There are several video files from which to chose. From the "PASCO" subdirectory chose one of the following: For elastic collisions pasco17, pasco18, pasco19, pasco20, pasco21, pasco22, pasco78, pasco79, pasco80, or pasco81; and for inelastic collisions pasco24, pasco25, pasco26, pasco27, pasco28, pasco29, pasco30, pasco82, pasco83, pasco84, pasco85, pasco86, or pasco87. The student should do one elastic and one inelastic experiment and perform the following for each.
With the VideoPoint software mark the position of the object as it moves as demonstrated in the "Instructions for using VideoPoint". It will me necessary to collect data for two carts, one for each object in the collision. The velocities before and after the collision should be constant. The velocities can be calculated by dividing the distance traveled by the object by the time of travel. This data is available in VideoPoind by taking the differences between the final and initial readings both before and after the collision. Knowing the masses and velocities is enough information to finish the calculations. A step-by-step procedure for using VideoPoint is at the end of the experiment.
1. Calculate the final velocities assuming the collision is elastic or inelastic as the case may be.
Find the percent error in agreement of these values with those obtained in the experiment.
2. Calculate the momentum of each object in the collision before and after the collision. Find the total momentum before and after the collision and find the percent error in agreement of these values.
3. Calculate the kinetic energy by of each object in the collision before and after the collision. Find the total kinetic energy before and after the collision and find the percent error in agreement of these values.
4. Calculate the coefficient of restitution for the collision
QUESTIONS:
1. Where did the kinetic energy go in the inelastic collision if it was not conserved?
2. Look at the data and estimate the time it took for the collision to occur. Using the fact that the impulse is equal to the change in momentum, estimate the forces involved in the collision.
3. Was it approximately true that momentum was conserved in both the elastic and the inelastic collisions?
4. In a one-dimension elastic collision of objects with equal masses, how do the velocities of the two objects colliding compare before and after the collision.
5. In a one-dimension collision that is not elastic but the objects do not stick together after the collision, can the final velocity of both objects be found by knowing only the initial velocity and masses of the objects?
6. Is it possible to have a collision that conserves kinetic energy and not momentum?
Start VideoPoint.
Click left mouse button while the pointer is anywhere inside the "about VideoPoint" dialogue box.
In the "open" dialogue box do the following.
Select the drive letter of the CD drive in which VideoPoint is located.
Select movies folder and the appropriate folder under movies (here the "pasco" folder).
Under filename select the appropriate file to be loaded.
Press "OK".
The "Number of points" dialogue box will appear. Make sure "2" is selected and press "OK". The movie and software should now be loaded.
Record the masses listed in the first frame of the movie.
On the menu bar select "Movie" and "Full Screen" using the left mouse button.
Record data -When the cursor is inside the movie screen it appears as a target. Place this target cursor on a point on one of the carts on the top track and press the left mouse button. Repeat this process for the other cart. The movie will advance one frame and the data is recorded. Repeat this process in the same order until all frames of the movie have been used. Be consistent and use the same point on the cart each time to record the data. Ignore any carts moving on lower tracks, they can be used for relative velocity experiments.
Calibrate the movie.
Move the cursor to the "meter stick" tool button at the left of the screen (6th button from top) and click the left mouse button.
The "Scale Movie" dialogue box appears. Select continue with the left mouse button.
Put the target cursor on the left end of the meter stick in the first movie frame and press left mouse button - repeat for the right end of the meter stick.
On the menu bar select "Movie" and "Normal Size".
Transfer the data
Observe the movie frame where the collision occurred and record the change in positions and elapsed time for the two frames immediately before and the two frames immediately after the collision
With cursor inside table area click left mouse button to select table.
Put mouse in title area of table and click and hold left mouse button
and drag the
table to top of window.
Place the pointer on lower right corner of table (cursor should be double arrow) and drag the corner of the table to make the table larger so all the data can be seen.
Mass of first car M1 = _______________
Mass of second car M2 = _______________
Before collision After collision
(primed values)
Distance traveled by first car D X1 = __________ __________
Time first car traveled D T1 =__________ __________
Velocity of first car V1 = D X1 / D T1 = __________ __________
Distance traveled by second car D X2 = __________ __________
Time second car traveled D T2 =__________ __________
Velocity of second car V2 = D X2 / D T2 = __________ __________
= _______________
% error __________
= _______________
% error __________
Momentum
p1 = M1V1 = ________ p2 = M2V2 = ___________
p1` = M1V1` = __________ p2` = M2V2` = __________
Total momentum before collision = p1 + p2 = _______________
% error _________
Total momentum after collision = p1` + p2` = _______________
Kinetic Energy
KE1 = 1/2M1V1² = ___________ KE2 = 1/2M2V2² = __________
KE1` = 1/2M1V1`² = __________ KE2` = 1/2M2V2`² = __________
Total KE before collision = KE1 + KE2 = ______________
% error _________
Total KE after collision = KE1` + KE2` = _______________
Coefficient of restitution 
= __________
Mass of first (large) car M1 = _______________
Mass of second (smaller) car M2 = _______________
Before collision After collision
(primed values)
Distance traveled by first car D X1 = __________ __________
Time first car traveled D T1 =__________ __________
Velocity of first car V1 = D X1 / D T1 = __________ __________
Distance traveled by second car D X2 = __________ __________
Time second car traveled D T2 =__________ __________
Velocity of second car V2 = D X2 / D T2 = __________ __________
= _______________
% error __________
Momentum
p1 = M1V1 = ________ p2 = M2V2 = ________
p1` = M1V1` = __________ p2` = M2V2` = __________
Total momentum before collision = p1 + p2 = _______________
% error _________
Total momentum after collision = p1` + p2` = _______________
Kinetic Energy
KE1 = 1/2M1V1² = __________ KE2= 1/2M2V2² = __________
KE1` = 1/2M1V1`² = __________ KE2` = 1/2M2V2`² = __________
Total KE before collision = KE1 + KE2 = _______________
% error _________
Total KE after collision = KE1` + KE2` = _______________
Coefficient of restitution 
= __________