15-Apr-2015: Impulse-Momentum Activity

Purpose: Using three impulse and momentum experiments, we were to convince ourselves that the impulse applied to an object is the area under a graph for a force acting over an interval of time and is equal to the change in momentum of the object after the collision.

Experiment 1: Observing Collision Forces That Change With Time

Procedure: To begin we set up our track so that a cart with a force sensor attached to it would collide into a springy bit of another cart clamped on the other end. The force cart has a rubber stopper replacing the hook on the sensor and springy cart is attached to a rod which is clamped to the table The carts should be set up such that the collision between the two carts happens with the rubber stopper and the springy bit. We did a couple test runs to make sure there was solid contact between the two ends. Then we placed a motion sensor on the force sensor cart side, with the positive direction reading in opposite direction of the cart's initial velocity.

The impulse-momentum theorem states that the impulse acting on the cart is equal to the amount of momentum change for the moving cart. So, by finding the change in momentum using the mass of the cart and the velocities before and after the collision, and the impulse by finding the area under the force vs. time graph, we can test whether impulse(J) = change in momentum (P).

Lab set up with carts placed at opposite ends.

Before starting the experiment we made sure that the force probe was calibrated horizontally and vertically. Then checked to make sure the motion sensor was reading the cart all the way through without any interference. We then began recording and graphing our data.

graph of velocity vs. time in green and force vs. time in blue

We compared our integral of the force vs. time graph to our change in momentum using the velocities from the velocity vs. time graph.

Results comparing impulse and change in momentum in an elastic collision

Results: Our results show that the Impulse = -.2268 which is nearly equal to the change in momentum =-.2452. Because the spring was not perfect, we can say that our results confirm we had a nearly elastic collision.

Experiment 2: A Larger Momentum Change

Procedure: We use the same set up as the first experiment, except we added 0.5 kg of mass to our cart in order to get a larger momentum change. We wanted to test whether the impulse and change in momentum still equaled to each other when using a more massive cart. We check to make sure the collision is solid again then begin recording our data.

graph of velocity vs. time in green and force vs. time in blue 

Using logger pro we found the integral of the force vs. time graph and compared to our change in momentum using the velocities before and after collision from green graph.

Results comparing impulse and change in momentum in elastic collision + mass

Results: Our results show that the impulse = -.827 which is very close to our change in momentum = -.793. Again because the spring is imperfect, we expected our result to not exactly reflect an elastic collision.

Experiment 3: Impulse-Momentum in an Inelastic Collision

Procedure: For this part, we wanted to examine the impulse-momentum theorem in a collision where the cart sticks to a wall and stops after the collision. We emulate this by replacing the springy bit on and the cart with clay attached to a vertical piece of wood clamped to the table, and replacing the rubber with a nail. We leave the extra 0.5 kg of mass on the cart and set up the track for the next collision. We begin recording data and wanted to see whether the impulse acting on the cart is equal to the change in momentum in inelastic collisions as well. 

graph of velocity vs. time in green and force vs. time in blue

Again we calculate the change in momentum and compare to the integral of the force vs. time graph for an inelastic collision.

results comparing impulse to change in momentum for an inelastic collision

Results: The impulse acted on the cart = -.408 which is very close to the change in momentum of the cart = -.371. Proves that J=change in P for inelastic collisions.

Conclusion/Uncertainty: After experimenting with two elastic collisions and one inelastic collision, we confirmed that the total net impulse acted on a cart, which is found by finding the integral of force over a interval of time, is in fact equal to the change in momentum of the cart for both elastic and inelastic collisions. The impulse-momentum theorem which states that J=change in P was accurately represented by all three of our results. However, our results were not perfectly equal due to a few possible uncertainties in our experiment. First, our track was not perfectly frictionless like we assumed in our calculations. Secondly, the spring bit for the first two experiments did not create a perfectly elastic collision. Also things like the accuracy our scale to measure the mass of the cart is +/- 1 g. But overall the experiments accurately represented the model that we were testing.