15-April-2015: Impulse Momentum Activity

     The purpose of this experiment was to test and confirm the impulse-momentum theorem. The idea was to calculate a cart's momentum and compare it with impulse by integrating a force vs time graph created by colliding the cart with something. This was because the impulse-momentum theorem says that impulse is equal to the change in momentum of an object There were 3 parts to this experiment.

Part 1

     The first part of the experiment consisted of a moving cart colliding with a stationary cart. The stationary cart had a spring like component sticking out from it that the moving cart would collide into. The idea is that in a perfectly elastic collision, the moving cart would crash into the stationary cart and bounce back with the same magnitude of momentum.
     The setup had a stationary cart being held in place with a clamp at one end of a level track.

 A motion sensor was placed at the opposite end of the track. A second cart was placed on the track. A force sensor was taped onto the cart, the force probe facing the stationary cart. An index card was placed on the back of the cart so the motion sensor could detect the cart's position easier.

The mass of the cart was weighed using a digital balance. Its mass was 692 grams. This was needed for later calculations. Now the experiment could begin.
     The motion sensor was activated and the cart was given a push toward the stationary cart. The moving cart collided with the springy part of the stationary cart and then bounced back toward the motion sensor. The motion sensor produced a velocity graph and the force sensor produced a force vs time graph. Below are the graphs.

Top graph: velocity vs time
Bottom graph: force vs time

     By taking the average velocity before and after the collision, the change in momentum was able to be calculated. Taking the integral of the force vs time graph gave a value for impulse. Below was the relationship that was being used to compare the data and sample calculations for this first experiment. Each experiment after this used the same calculations so they will not be shown.

     The calculated change in momentum was 0.7541 N*s and the value given from the force vs time graph for the impulse was 0.7481 N*s. These very close numbers, off by 0.006, suggest the impulse-momentum theory holds true for this experiment.

Part 2

     The same set up was used for Part 2, except 400 grams of mass was added to the cart. This experiment produced very similar graphs to Part 1, shown below.

Using the same methods from part 1, the calculated change in momentum was 1.298 N*s and the impulse obtained from integrating the force vs time graph was 1.248 N*s. These two numbers are further apart than the ones in part 1, but they are still very close. This suggests that the impulse-momentum theorem holds true for more massive objects in a similar experiment.

Part 3

     For part 3, the impulse-momentum theorem was examined in an inelastic collision. The same cart with the added 400 grams of mass was used but this time a nail was put in place of the rubber stopper on the force probe, and some clay was put in place of the stationary cart. 

     It was predicted that the impulse would be smaller than the impulse of the previous two parts since the final velocity would be zero. It was also predicted that the impulse and momentum would be nearly equal as they were in the previous two parts.

     The cart was given a push and it collides with the clay and stops. Below are the graphs that were produced. The top graph is the velocity graph and the bottom is the force vs time graph. The same techniques were used to analyze these graphs as in the first two parts.

     The calculated change in momentum was 0.4175 N*s and the impulse from the graph was 0.4275 N*s. Again, this experiment resulted in numbers very close to each other, only off by 0.01. 

     The data for all three experiments was very promising. All three showed a change in momentum that was very close to the impulse obtained from the area under a force vs time curve. Although not perfect, these results suggest the impulse-momentum theorem to be true. Reasons for the imperfection could be attributed to friction between the cart and track, since it was assumed it was a frictionless surface. Also, in the first two parts, the stationary cart's spring bumper was not perfect and could not send the moving cart back at the same speed in which it came.