3.1
Physics 2010
Conservation of Momentum and Energy
Experiment 3
In one dimension (1D), the momentum p of an object of mass m and velocity v is
p  mv . In 1D, we represent the direction of travel by the sign of v and p. Usually, the
direction to the right is chosen as positive and to the left is negative, but this is purely a
matter of convention. The kinetic energy of an object of mass m and velocity v (v in 1D,

v in 2D or 3D) is defined as KE  21 mv 2 .
Momentum and energy are useful concepts because these quantities are
conserved, that is, they do not change with time. You cannot create or destroy energy,
you can only change it from one form to another [kinetic energy, potential energy, heat,
acoustic energy (sound) etc.]. Likewise, you cannot create momentum out of nothing, nor
can you get rid of it - you can only transfer it from one body to another. For instance, a
traveling car has a lot of momentum. When the brakes are applied and the car stops, its
momentum is actually transferred to the whole earth (through the wheels touching the
road and through the air hitting the car) ! If the car strikes an unlucky pedestrian, then the
car's momentum is partly transferred to the pedestrian and partly transferred to other
things it comes in contact with, including the earth.
If a moving object collides with another object and the total kinetic energy of the
two objects does not change - that is, it remains the same before and after the collision then the collision is elastic. If some of the kinetic energy of the objects is transformed
into heat or other forms of energy, then the collision is inelastic. Most collisions
encountered in everyday life are inelastic. Notice that kinetic energy is only conserved in
the special case of elastic collisions. In general, kinetic energy is not conserved.
However, momentum is always conserved, regardless of whether the collision is elastic or
inelastic.
In this lab, we will study the collision of gliders on an air track. First, we will
study an inelastic collision, in which the two gliders stick together after the collision.
Then we will study a (nearly) elastic collision, in which the gliders are fitted with rubber
bumpers so that they bounce off each other and very little of their kinetic energy is lost to
friction.
Part 1. Preliminary set-up.
Begin by leveling the air track. Turn on the air supply, gently place a glider on the
track, and adjust the track's feet so that the glider remains stationary. In this lab, you will
be attaching various accessories to the ends of the gliders (rubber bumpers, pin holders,
wax cups). Unfortunately, placing something on one side of a glider makes it unevenly
weighted so that it tilts slightly toward the heavier side. This causes the air cushion under
the glider to be non-uniform, and, as a result, the glider will slowly accelerate to one side,
even though the track is perfectly level. To correct for this effect, make sure that the
gliders are symmetrically loaded at all times. If you place a bumper on one end, place an
identical bumper, or something of equal weight, on the other end.
We will be measuring the speed of the gliders by using the photogates in GATE
mode. A card, of length x  10.0 cm , is placed on top of the gliders. When a glider
02/06/16
3.2
passes through the gate, the card interrupts a photosensor for a time t , and the speed of
x
the glider is
. If the track is level, a glider should have a constant velocity on the air
t
track, but it usually slows down slightly because of air resistance. To try to see this
effect, and to get an idea of the uncertainty in measured values of t , we will begin by
sending a glider through two gates and comparing the times through each gate.
Place two photogates over the track, about 0.5 m apart and near the center of the
track. Set the timer to GATE and hit RESET. Gently push the glider down the track so
that it passes through each gate once and stop the glider at the other end. The timer will
display the time through the first gate t1. Press READ to get the total time, t1  t 2 ,
spent traversing both gates. Record t1 , your computed t 2 , and the quantity
t 2  t 1
. Repeat this experiment a few times and display your data in a table. The
t 1
average value of
t 2   t 1
t 1
is a good estimate of the fractional uncertainty of t . The
 t 2  t 1 
percent uncertainty is 
  100% . The final uncertainty in t , written ( t ) ,
t 1


is the fractional uncertainty times t avg .
Part 2. Inelastic Collisions
If two objects collide and the only forces on the colliding objects are the forces
which they exert on each other (no forces from the outside), then the total momentum of
the two objects is the same before and after the collision. If mass m1 has velocity v1 and
mass m2 has velocity v2, then the total momentum of two masses is
p tot  p1  p 2  m1 v1  m 2 v 2 . If one or both gliders scrapes against the air track
during a violent collision, then there is an external force on the gliders along the
direction of travel and the momentum of the gliders will not be conserved (even though
momentum of the gliders + air track + rest of the universe is always conserved).
Insert the pin attachment on one glider and the wax cup attachment on another
glider as shown below(remember to keep the gliders symmetrically loaded). Now, when
the gliders collide, the pin will stick in the wax cup and the gliders will stick together.
Place a card for blocking the photogate on the glider with the pin (we'll call it glider 1).
Do NOT place a card on the glider with the wax cup (glider 2). Place two 50 gram
masses on each glider (100 grams on each glider), weigh the gliders and record their
masses as m1 and m2.
02/06/16
3.3
gate 1
card
pin
glider 1
gate 2
wax cup
glider 2
air track
Practice pushing glider 1 gently so that it collides and sticks to an initially
stationary glider 2. Note that the final velocity is much smaller than the initial velocity.
Practice until the collision does not produce a noticeable click or scraping sound - the
sound would indicate that a glider has contacted the air track.
After practicing a few times, prepare to perform the following experiment one
time only. Keep the timer set to GATE mode and RESET the timer. Place glider 2 at rest
between the two gates and near gate 2. Push glider 1 so that it passes through gate 1,
collides and sticks to glider 2 and passes through gate 2. Record t1 and t 2 . Compute
x
x
and record the initial and final velocities v i 
and v f 
. Determine the initial
t 1
t 2
and final momenta, p i  m1v i and pf  ( m1  m2 ) vf . [You cannot repeat this
experiment, because you can never be sure you are pushing glider 1 with the same initial
speed.]
Compare the initial and final momenta by computing the percent discrepancy:
momentum discrepancy =
p final  p initial
 100%
p initial
What sources of experimental error might account for this discrepancy?
Repeat this experiment and your calculations with the two 50 gram masses on
glider 1 but not on glider 2. Be sure to use the new masses of gliders 1 and 2 in your
calculations.
Part 3. Elastic Collisions
In elastic collisions, both momentum and kinetic energy are conserved. Replace
the pin and wax cup holders on the gliders with a flat metal contact on the end of glider 1
and a rubber band contact on glider 2. (Remember to load the gliders symmetrically,
even though the drawing below shows them unevenly loaded). Place a gate card on both
02/06/16
3.4
gliders and place two 50 gram masses on each glider (100 grams on each glider).
Measure and record the masses m1 and m2 of the gliders.
Flat metal contact
Glider 1
Rubber band bumper
Glider 2
Practice sliding glider 1 into glider 2. If the two masses are almost the same and if glider
2 is initially stationary, you should see that glider 1 stops almost completely and glider 2
moves off with a velocity equal to the initial velocity of glider 1.
Place glider 2 about half-way between the two gates. RESET the timer and push
glider 1 so that it passes through gate 1, collides with glider 2, and glider 2 passes through
gate 2. Stop glider 2 so that it does not pass through gate 2 more than once. Record the
x
times t1 and t 2 . Denote the initial velocity of glider 1 as v1i 
. The initial
t 1
x
velocity of glider 2 is zero. The final velocity of glider 2 is v 2 f 
. The final
t 2
velocity of glider 1 may be so small that we can assume that it is zero. If it is not small,
then measure its speed by timing its travel over a known distance (say, 10cm). (Ask
your instructor for a stop watch if you need to do this.) Perform this experiment only
once. As before, you cannot repeat this experiment because you can never be sure that
are pushing glider 1 with the same initial speed.
The initial kinetic energy of both gliders together is
KE initial 
1
m1v12i .
2
(Glider 2 is not moving initially so its KE is zero.)
The final kinetic energy of both gliders is
KE final 
02/06/16
1
1
m1v12f  m 2 v 22 f .
2
2
3.5
The initial momentum is
p initial  m1v1i .
The final momentum is
p final  m1v1f  m 2 v 2 f .
Compare the initial and final momenta and kinetic energies and compute the
percent discrepancies. What experimental errors might account for the discrepancy?
Additional questions to discuss in your lab report:
1. In part 2, for the inelastic collision in which the masses were different, calculate the
total kinetic energy before and after the collision. How much kinetic energy was lost
during the collision. What happened to this energy?
2. In the same inelastic collision, which had the largest velocity change, the larger mass
glider or the smaller mass glider? What are the implications for automobile safety?
02/06/16
3.6
Physics 2010
Pre Lab Questions
Experiment 3
1. Two objects of mass m1 and m2 are each moving to the right along the x-axis with
speeds v1 and v2. Write expressions for the total momentum and the total kinetic
energy of the two objects. How would you change your answer if object 2 were
headed towards object 1?
2. What is the term for a collision in which kinetic energy is lost to heat or noise?
3. For an isolated system, is total momentum always conserved?
4. Why is it important to keep the gliders evenly weighted in this experiment?
5. In part 3 of the lab, after measuring the initial and final kinetic energy, you are asked
(among other things) to compute their percent discrepancy. What is the mathematical
expression for this percent discrepancy? Can it ever come out negative?
6. Dry lab.
02/06/16