PERFECTLY INELASTIC COLLISIONS
OBJECTIVE:
To verify the principle of conservation of linear momentum and compute the amount of kinetic energy converted to heat
energy for inelastic collisions.
APPARATUS:
Air track
Computer
Two photogates
Flag
Small glider
Balance
Large glider
INTRODUCTION:
Perfectly inelastic collisions are when the two objects stick together after the collision. In perfectly inelastic collisions the
momentum of the system is conserved but there is a change in the kinetic energy of the system. Both the projectile speed
before the collision, v1, and the combined speed after the collision, v2, are measured.
Conservation of momentum implies:
p1 = p 2
(initial momentum = final momentum)
m1v1o + m2 v 2 o = m1v 2 + m2 v 2
Since mass 2 is initially at rest, v 2 o = 0, and
m1v1 = (m1 + m2 )v 2
Equation 1
Where m1 is the projectile mass and m2 is the target mass. Therefore, the final speed is
⎛ m1
v 2 = ⎜⎜
⎝ m1 + m2
⎞
⎟⎟v1
⎠
Equation 2.
Equation 2 implies that a graph of the values of v versus the values of v would yield a straight line with
2
1
m1
slope =
. This slope is compared with the ratio of the directly measured masses using the digital scale.
m1 + m2
The kinetic energy before and after the collision should NOT be equal or
1
1
2
2
m1v1 ≠ (m1 + m2 )v 2
2
2
Equation 3.
PROCEDURE: (Make sure the air is on before you begin – ask the lab assistant)
1. Click the Physics folder. Then double click the Inelastic Collisions icon. Measure and record the mass of each glider
on the data table.
6. Position the target glider (small glider) between the two photogates, near the second gate. The projectile glider (large
glider) should be placed to the left of the first photogate. The flag on the projectile glider must pass completely through
the first gate before the collision and completely through the second photogate after the collision. The velcro ends of
the gliders must face each other. Click on the COLLECT button.
7. Launch the projectile glider from a point before the first photogate while holding the target gate at rest. Release the
target glider before impact. Catch the coupled gliders before they rebound from the other end of the air-track.
8. Repeat step 7 six more times for different launch speeds. You can vary the launch speeds by pressing the launch glider
against the rubber band launcher and displacing the rubber band various lengths.
9. Now click on the STOP button. Record the values for v1 and v2 on the data table.
PERFECTLY INELASTIC COLLISIONS LAB SHEET
DATA TABLES:
INCLUDE UNITS
V1
V2
GLIDER TYPE
MASS
SMALL
LARGE
INCLUDE FLAG
Using graphical analysis make a graph of V2 vs. V1 and
find the slope of that line. Print out graph.
CALCULATIONS: SHOW ALL WORK INCLUDE ANSWERS ON RESULT TABLE
m1
1. Calculate the actual ratio
Compare the values to the slope of the graph using the percent error formula.
m1 + m2
2. Pick any one of the collisions and verify conservation of momentum using equation 1. Compare the momentum
before the collision to the momentum after using the percent difference formula.
3. Using the same collision point as in 2, calculate the kinetic energy before and after the collision. Compare these
values using the percent difference formula. The percent difference is the kinetic energy transformed into heat.
RESULTS TABLE: INCLUDE UNITS
ACTUAL
RATIO
SLOPE
FROM
GRAPH
%
ERROR
MOMENTUM
BEFORE
CONCLUSION:
TURN IN LAB SHEET AND GRAPH
MOMENTUM
AFTER
%
DIFFERENCE
KINETIC
ENERGY
BEFORE
KINETIC
ENERGY
AFTER
PERCENT
DIFFERENCE