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NORTHERN ILLINOIS UNIVERSITY
PHYSICS DEPARTMENT
Physics 253 – Fundamental Physics Mechanics
Lab #9 Collisions
Meet in FR 233.
Sections A, B, C, G: Tuesday Oct. 25; Sections D, E, T: Thursday Oct. 27.
Read Giancoli: Chapter 9
Lab Write-up due Tue. Nov. 1 (Sections A, B, C, G); Thur. Nov. 3 (Sections D, T)
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 9 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
the positive direction, the velocity is positive, and if it is moving in the negative direction,
the velocity is negative. An object at rest has a velocity of 0.
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 (m1 and m2) and
velocities (v1 and v2) moving only in one dimension, the total momentum P is
P  m1v1  m2v2
(2)
If there are no forces acting on a set of objects other than the forces between the
objects in the set, the system is called an isolated system. 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
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momentum is Pi and the final total momentum is Pf, conservation of momentum tells us
Pi=Pf.
Objects in motion also possess kinetic energy. Kinetic energy K is a scalar
quantity that is never negative. It depends on the mass and velocity according to
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(3)
K  mv 2
2
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
1
1
2
2
(4)
 K  m1v 1  m2v 2
2
2
In certain collisions between objects that only involve a conservative force, such as an
ideal spring, the initial total kinetic energy Ki equals the final total kinetic energy Kf. This
type of collision is called an elastic collision.
Other collisionsare called inelastic and involve some loss of energy during the
collision due to deformation of the objects, sound, or friction. In an inelastic collision,
the final total kinetic energy of the system is always less than the initial total kinetic
energy. 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: vf =
v1f + v2f. We can write Eq. (2) for a completely inelastic collision as
m1v1i + m2v2i = m1v1f + m2v2f = (m1 + m2) vf.
(5)
Apparatus
An air track is an aluminum tube with many small holes to release compressed air,
and provides a nearly frictionless surface. In this experiment the track is level, and there
are two carts: a large cart of mass m1 and length l1 and a small cart of mass m2 and length
l2. 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. Your TA will give you the
equations you need to calculate the errors on your calculated quantities.
Preliminaries:
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(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.
(2) Measure and record the mass (m1 and m2) and length (l1 and l2) 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 of
the large cart and its uncertainty 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 both 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
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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?
(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 are
elastic or inelastic.