4/16/15: Impulse - Momentum Lab 14

Purpose: The impulse-momentum theorem states that the change in momentum for a moving cart is equal the net impulse acting on the cart (∆p = J). Our job is to test this idea by performing three experiments.

Expt 1: Observing Collision Forces That Change With Time

A dynamics cart with its spring plunger extended is clamped to the table using a rod and c-clamp. On the other end of the track is a force sensor mounted to another dynamics cart with a rubber stopper in place of the force sensors hook. Be sure to level the plunger with the rubber stopper so they can correctly collide with each other. 







For the first part of this experiment, we will be measuring a non-constant force over a time interval ∆t. In order to verify the impulse-momentum theorem (∆p = ∫ Fdt), we will need to measure the mass of the cart and use logger pro to generate a force vs. time graph and a velocity vs. time graph, as we will be needing the velocity of the cart right before and after the collision. Once the apparatus has been set up, open the file called Impulse and Momentum (L08A2-2), calibrate the force sensor and re-attach it the moving dynamics cart. Once ready, zero the force probe and hit collect to begin graphing. Give the cart a push toward the stationary cart and let it collide with the plunger and bounce back. Once logger pro has generated a force vs. time graph, open up an axis that shows velocity vs. time.

By analyzing the graph of force vs. time using an integral fit, the impulse imparted (∫ Fdt) on the cart was 0.7481 N*s.

Using the final and initial velocity values of the cart as well as the mass, the change in momentum (∆p) can be calculated. ∆p = 0.754 N*s

Since J = 0.7481 N*s and ∆p = 0.754 N*s, we can say the impulse does closely equal the change in momentum.

Expt 2: A Larger Momentum Change

Using the same set up an in part 1, we added mass to the cart and repeated the experiment to see if the impulse-momentum theorem still held true.

Again by analyzing the force vs. time graph using an integral fit, we can obtain the impulse imparted on the cart which equaled 1.248 N*s

Using the final and initial velocity values of the cart as well as the new mass, the change in momentum (∆p) can be calculated. ∆p = 1.298 N*s

Again J = 1.248 N*s and ∆p = 1.298 N*s, we can say the impulse does closely equal the change in momentum.

Expt 3: Impulse - Momentum Theorem in an Inelastic Collision

In this experiment we used the same set ups as in part 1 and 2, except this time a wooden block with a blob of clay will be in place of the stationary dynamics cart. A nail will be attached to the rubber stopper on the force sensor hook as well. We kept the mass of the cart the same as in part 2 (1.092 kg). 

We hit collect on logger pro and gave the cart a push towards the wooden wall and analyzed a force vs. time and velocity vs. time graph.

Using an integral fit, we measured the impulse to be J = 0.4276 N*s

Since the final velocity of the cart is 0 m/s we analyzed our velocity vs. time graph and found the initial velocity of the cart to be 0.3859 m/s. Our change in momentum ∆p = 0.4225 N*s

Because J = 0.4276 N*s and ∆p = 0.4225 N*s, we can verify the impulse-momentum theorem once again hold true for this experiment.

Conclusion:

For this lab, we wanted to verify the impulse-momentum theorem (∆p = J). We were able to do this by performing three different experiments: two elastic collisions, and one in-elastic collision using dynamics carts. In all three experiments, the impulse imparted on the cart nearly equaled the change in momentum of the cart. If the experiment was perfect, the two values would be exactly the same. Some error within the experiment could have been due some slight friction on the track even though its supposed to mimic a frictionless surface. Another source of error is from the bumper on the stationary dynamics cart. In a perfectly elastic collision, the cart would recoil with exactly the same momentum it had before the collision. Over all, we can conclude the theorem holds true.