Linear Momentum

     Measurements of velocity and mass of two objects colliding, support the
conservation of linear momentum. The dynamics of different masses distinguish
velocity values experimentally. Video recordings of two colliding masses can be
manipulated to extract frames displaying distance verses time. Computer software
enables us to derive the velocity. Different masses were tested to determine an
increase, decrease, or equal effect. From this data, we ultimately derive the
momentum of each cart and test the Law of Linear momentum. The following trials
were measured: 1. An elastic collision with a cart moving at constant speed with
a cart of equal mass originally at rest; 2. An elastic collision with a car
moving at constant speed and a cart of one-third the mass originally at rest. 3.

An elastic collision with a cart of three times the mass originally at rest; 4.

An inelastic collision with a cart moving at constant speed and a cart of two
times the mass originally at rest. Procedure Materials: *quick cam *software
*two carts of equal mass *two 500g weight blocks *track Steps: 1. Set-up camera
according to the correct settings noted in 3.4 (pp. 19) 2. Establish four points
of reference visible in the camera frame. Place the initial motionless cart at
the second reference point from the end opposite of the oncoming cart. Record an
elastic collision with a cart moving at constant speed with a cart of equal mass
originally at rest. 3. Save the video (refer to 3.4 pp.19 for instructions). 4.

Open video point to begin analysis of the motion (3.4.1 pp. 19-20). 5. Construct
a distance vs. time graph, and a velocity vs. time graph for (A) the cart in
motion before the collision (B) the cart(s) in motion after the collision. Three
sets of the distance and velocity graphs may be required. 6. On the velocity vs.
time graph, find the average velocity; click the "F" button on the top
right-hand side of the graph and select "average". Print both graphs -
distance, velocity. 7. Repeat this procedure from the step number two for the
entire four scenarios. 8. The mass of each cart is 500 grams. The mass of each
block is 500 grams. Results In the first scenario, with both masses equal,
momentum is virtually conserved with a P of 0.0035kgm/s. The second scenario
contains a cart three times the mass as the other. Our information concludes
that P equals 0.0735 as the initial cart continues in the same direction after
collision. So far our measurement supports the law of momentum conservation. The
third scenario involves the opposite mass components of the second scenario; the
initial mass in motion is one-third the mass of the motionless cart. The P is
-0.1655kgm/s as the original moving mass changes direction after collision. The
collision in the fourth scenario is inelastic. The components stick together and
have the same ending velocity although starting masses were different; the cart
at rest is one-half the mass of the cart moving towards it. The resulting P
equals -.3013kgm/s. This indicates a large difference in the initial momentum
verses the final momentum. In the video, the two carts came to rest 20cm from
collision. The experimental results vary in accuracy according to the
theoretical results. In an elastic collision, one expects the momentum to be
conserved. However, we found our P off by a range of 0.0035kgm/s to
-0.1655kgm/s. We found this error partially due to the points that were graphed.

Some exceeded the range of motion that was needed to calculate. The other margin
of error may be due to the small distance between the reference points. In the
inelastic collision, energy is lost, perhaps to thermal energy. This might
explain the large P.