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NORTHERN ILLINOIS UNIVERSITY
PHYSICS DEPARTMENT
Meet in FR 233.
Sections A, B, C: Tuesday Apr. 5; Sections D, E, F: Thursday Apr. 7.
Read Giancoli: Chapter 9
Lab Write-up due Tues Apr 12 (Sections A, B, C); Thurs Apr 14 (Sections D, E, F)
Objective
In this laboratory you will use an air track to create and analyze elastic collisions and inelastic collisions. First we will review the theory behind collisions (Chapter 10 in your text). Then we will describe the apparatus used for these collisions. Afterwards, you’ll perform and analyze the collisions.
Theory
Velocity is the time rate of change of position of an object. If the length of an object and the time it takes to pass a point are both known the velocity is given by, v  l
 t
(1)
The sign of the velocity depends on the direction of the object. If the object is moving in
Momentum p is the product of mass m and velocity v . Since velocity is a vector and has direction, so does momentum. For two or more interacting objects, the total momentum is just the sum of the individual momenta. For two masses ( m
1
and m
2
) and velocities ( v
1
and v
2
) moving only in one dimension, the total momentum P is
P  m
1 v
1
 m
2 v
2
(2)
If there are no forces acting on a set of objects other than the interaction between isolated syste m. In any isolated system the total momentum of the set of objects is constant. We say that the total momentum in an isolated system is conserved . During a collision the time is so short that external forces do not have much effect on the momentum of the system. This allows us to describe all collisions as isolated systems and apply conservation of momentum. If the initial total momentum is
P i
and the final total momentum is P f
, conservation of momentum tells us P i
=P f
.

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Objects in motion also possess kinetic energy. Kinetic energy K is a scalar quantity that is never negative. It also depends on the mass and velocity according to
K 
1
2 mv 2
(3)
Like total momentum, the total kinetic energy of a system is just the sum of the individual kinetic energies. For a system of two objects the total kinetic energy is
 K 
1
2 m
1 v 2
1

1
2 m
2 v 2
2
(4)
In certain collisions between objects that only involve a conservative force, such as an ideal spring, the initial total kinetic energy K i
equals the final total kinetic energy K f
. This elastic
Other collisions are called collision. inelastic and involve some loss of energy during the collision due to deformation of the objects, sound, or friction. The final total kinetic energy is always less than the initial total kinetic energy of the system. A completely inelastic collision occurs when the two objects collide and stick together. This means that the two objects leave the collision with identical velocities: v f
= v
1f
+ v
2f
. We can write
Eq. (2) for a completely inelastic collision as m
1 v
1i
+ m
2 v
2i
= m
1 v
1f
+ m
2 v
2f
= (m
1
+ m
2
) v f
. (5)
Apparatus
An air track is an aluminum tube with many small holes to release compressed air and provide a nearly frictionless surface. In this experiment the track is level, and there are two carts: a large cart of mass m
1
and length l
1
and a small cart of mass m
2
and length l
2
. One cart has a bumper at one end to provide elastic collisions. The carts can also be positioned with Velcro between them to create completely inelastic collisions.
Two photogates are positioned over the track and can measure the time
 t that the cart passes the beam. The times can be read from the computer attached to the photogates. The photogates only record the elapsed time between the start and stop of the beam. The experimenter must determine the direction of motion. With the carts and the photogates we can study the velocities involved in both elastic and inelastic collisions.
Data Collection
You must show all your calculations in the Analysis section below to your TA before you leave the lab. This includes propagation of error calculations.
Preliminaries:
(1) Check that the computer is on and running the Logger Pro program. With the computer and airtrack on, confirm that the red light on each photogate flashes as the cart passes through the photogate.

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(2) Measure and record the mass ( m
1
and m
2
) and length ( l
1
and l
2
) for the large and small carts respectively (as well as their uncertainties).
(3) Place the large cart at one end of the track. Push the cart firmly, but not too hard, so that it passes through both photogates. Record the times from the computer, and estimate the uncertainty in these measurements.
Two Elastic Collisions:
(4) Place the small cart in the middle of the track with the spring facing the large cart.
Place the large cart at one end and push it through the first photogate toward the small cart. After the small cart passes through the second gate lift it off the track before it hits the large cart returning from the bumper.
(5) After the large cart passes through the second photogate, lift it off the track. Record the first time from the first photogate, and both times from the second photogate (as well as an estimate of their uncertainties). These will be used to calculate velocities.
(6) Repeat Steps (4) & (5) with the large cart in the middle instead of the small cart.
Two Inelastic Collisions:
(7) Reverse the cart with the spring so it faces away from the other cart. Place Velcro strips on the sides of the carts that face each other.
(8) Repeat Steps (4) through (6), but collect only one time measurement from each photogate.
(9) Measure and record the length of the two carts stuck together.
Analysis
(1) Using Eq. (1), find the velocity and its uncertainty of the large cart as it passed through each photogate in Step (3). Also, for each velocity, find the kinetic energy
(and its uncertainty) of the large cart using Eq. (3).
(2) For each collision (Steps (5) & (6) and both collisions in Step (8)), use the length and time information to find the velocity (using Eq. (1)) and kinetic energy (and their uncertainties), of each cart before the collision and after the collision. Is the total kinetic energy of the carts before the collision equal to the total kinetic energy of the carts after the collision? Do they agree to within your uncertainties? Is conservation of energy being violated? Where (and how much) is the missing energy going? What type of energy is this missing energy?

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(3) From Steps (5) & (6), find the total momentum and its uncertainty for the carts before and after each collision using Eq. (2). Do the same from Step 8 for the final momentum and its uncertainty from the collisions using Eq. (5). Is the total momentum of the carts before the collision equal to the total momentum of the carts after the collision? Do they agree to within your uncertainties? Is conservation of momentum being violated? Where (and how much) is the missing momentum going?
What type of momentum is this missing momentum? Explain why these collisions elastic or inelastic.