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Experiment 7 ~ Conservation of Linear Momentum
Purpose:
The purpose of this experiment is to reproduce a simple experiment demonstrating the
Conservation of Linear Momentum.
Theory:
The momentum p of an object is the product of its mass and its velocity:
p = mv
Momentum is a vector quantity, since it comes from velocity (a vector) multiplied by mass (a
scalar). The law of conservation of momentum states that the total momentum of all bodies
within an isolated system,
p total
= p1 + p 2
is constant. That is, if the total momentum has some initial value p i
, then, whatever happens
later, the final value of the total momentum p f
must equal the initial value. So we can write the
law of conservation of momentum like this:
p f
= p i
Conservation of momentum is usually studied in problems that involve collisions. In this
experiment, you’ll look at collisions between two gliders on an air track. You will measure the
final momentum of an initially stationary glider, struck by another glider which is initially
moving. You’ll do this experiment for two different types of collisions, elastic and inelastic.
Elastic collisions are ones where kinetic energy is conserved (the objects bounce off each other
without losing any energy). Inelastic collisions (e.g., if the objects get stuck together) do not
conserve kinetic energy. The kinetic energy of an object is defined as
where m is the object’s mass and v is its velocity. Kinetic energy is not a vector: it’s a scalar, and
its units are Joules (J).
Part I: Inelastic Collisions
Equipment:
Before you begin this experiment, you have to make sure the air track is level. First, turn the air
supply on. Place a glider in the middle of the track with no initial velocity. Adjust the leveling
screws until the glider remains in its initial position, not accelerating in either direction. The
glider may oscillate slightly about its position. This movement is caused by air currents from the
air holes in the track and should be considered normal.
Figure 1 illustrates the experimental method used for observation of inelastic collisions.
Glider 2, fitted with a Velcro impact pad (to make the gliders stick together!), will be positioned
at rest between Photo gate 1 and Photo gate 2. Glider 1 will be fitted with a measurement flag
and a needle.
Experiment:
For this part of the lab you will use the laptop connected to your set up. Save the Data Studio file
to the desktop. The .ds file can be downloaded from the Physics lab site at:
http://umsl.edu/~physics/lab/mechanicslab/11-Lab7.html. Once you have the laptop on and
the sensors plugged in you can double click on the saved file to open the Data Studio program. If
you need to find it later the program can be found in the ‘Education’ folder under the programs
in the start menu. To start taking measurements, click on the run button on the upper tool bar.
The lab TA will provide more instruction. If you make a mistake with the program you can start
over by closing the program without saving and opening it again from the Desktop.
Start recording the data for the first measurement.
Give Glider 1 a push. As it passes through Photo gate 1, a time interval (the “before” time) will
be measured. The velocity and momentum of Glider 1 can be computed from time data measured
and the mass of the glider.
Once Glider 1 strikes Glider 2, the two should stick together. The resulting momentum of the
coupled Gliders 1 and 2 can be computed from their total masses and the velocity measured at
Photo gate 2 (the “after” time). Once the gliders have stuck together, you can treat them as a
single object. Since the recorder is measuring time, the velocity recorded is automatically
computed using the 2.5 cm flag width (∆x).
Do this experiment a few times, and record your data.
Figure 1
Part II: Elastic Collisions
Equipment:
Figure 2 illustrates the experimental method used for observation of elastic collisions. In
this part of the experiment, you’ll observe the momenta (plural of momentum!) of a pair of
gliders before and after an elastic collision. Keep the photo gates in the same positions as in the
first part of the experiment. Remove the Velcro pads from the gliders. Attach rubber bumpers to
Gliders 1 and 2, and then position Glider 2 at rest between Photo gate 1 and Photo gate 2. Both
Gliders 1 and 2 will be equipped with vertically positioned-measurement flags.
Experiment:
Clear the previous data runs. Make sure that Glider 2 (the one that is going to be hit) is
placed between the two photo gates. Glider 1 should be outside the photo gates (see Figure
2).The first time measurement (“time before”) will be made by giving Glider 1 a push. Push it
gently (we’ll explain why in a moment). As Glider 1 passes through Photo gate 1, a time interval
will be measured. The initial velocity, momentum and kinetic energy of Glider 1 can be
computed from the velocity measured, and from the mass of Glider 1. Now, this is why you
want to push Glider 1 gently. You want it to hit Glider 2 so that Glider 2 will start moving, but
Glider 1 will stop moving. Think of a situation where one pool ball hits another and then stops –
but the second ball, the one that was hit, starts moving. That’s what you want to do with the
gliders. Basically you are transferring all the kinetic energy of Glider 1 to Glider 2!
The second velocity you will measure is the velocity of Glider 2 as it passes through the second
photo gate. This is our “time after”. The momentum and kinetic energy of Glider 2 can be
computed from the velocity measured, and from the mass of Glider 2.
Figure 2
Data and Calculations:
m 1
= Kg m 2
= Kg
Equation for initial and final momentum:
(mv) (^) o=
(mv) (^) f =
Equation for initial and final kinetic energy:
KEo =
KEf =
v (m/s)
=d/t
mv (Kg m/s)
(momentum)
mv
2 (J)
(kinetic energy)
Before After Before After Before After
Part II: Elastic collisions
- For each run of your elastic collision experiment, calculate the percent difference between the
initial momentum and the final momentum. Does your data indicate conservation of
momentum? Is the “before” velocity of Glider 1 equal to the “after” velocity of Glider 2? Why or
why not?
- For run of your elastic collision experiment, calculate the percent difference between the
initial energy and the final energy. Does your data indicate conservation of energy?
- List some possible source of error in this part of the experiment. Are these sources of error
random or systematic?
mv (Kg m/s)
(momentum)
Before After
% difference
mv
2 (J)
(kinetic energy)
Before After
% difference
