19-April-2017: LAB 14: Physics 4A Impulse-Momentum activity

Eric Chong

LAB 14: Physics 4A Impulse-Momentum activity

Lab Partners: Lynel Ornedo, Nina Song, and Joel Cook

Purpose: Observe/verify the impulse-momentum theorem.

Introduction/Theory: The impulse-momentum theorem states that the change in momentum is equal to the net impulse. Impulse is also equal to the amount of force applied times the change in time. Using this idea, we can test it by measuring the area under the curve of a force vs. time graph for the collision of a cart. We can then measure the change in momentum after measuring the cart's mass and its velocity before and after the collision with a motion sensor. Through calculating both the area under the curve of the force vs. time graph and calculating the change in momentum through the change in velocity, we can verify the impulse-momentum theorem. Afterwards, we can also test what happens to the momentum when the collision is inelastic, or in other words, when the cart is stuck to the clay on a wooden post when it collides. We can use the same procedure and examine the impulse-momentum theorem for this case. In a collision, the force exerted on the cart is very large, since it essentially reverses the cart's motion, and is also very quick, possibly less than even half a second. Since this lab has a springy type of extension used for the collision, the maximum magnitude of the force would be when the extension is compressed the most.

Procedure: First we fastened the force probe on the cart so that a rubber stopper is extended in front of the cart. We then attached an upside down cart to a pole attached to the table so that the cart's springy extension could collide with the force probe's rubber stopper. The cart is on top of a relatively frictionless, level track, with a motion sensor at the end opposite the end with the upside down cart. Here is what the setup looks like:

Using LoggerPro, we used an experiment file to help setup the necessary graphs and sensor properties, and making sure that the push on the force probe is positive and that the velocity toward the motion detector is positive. Before we ran the test, we measured the cart's mass, which turns out to be 641 grams. We calibrated the force probe using the hook screwed into the force sensor and holding the sensor vertically with a certain mass attached to it and without it, and then zeroing the sensor after it is horizontal and attached to the cart.

Finally, we started the experiment by pushing the cart in order to get it moving and recording its velocity, and then observing the collision and measured the force with the force probe. We ended up with a graph that looks like this:

As expected for the initial appearance, it seems that the velocity changes from negative (away from the sensor) to positive (toward the sensor). The force also is very high and applied very quickly, as it was not even half a second. We then took the area underneath the force vs. time curve by taking the integral to measure the change impulse.

As seen, it seems that the impulse is 0.4132 N*s. We then looked at the velocity vs. time graph and observed the initial and final velocity. The measurements we used were -0.325 m/s, just before the collision, and 0.306 m/s, right after the collision. We then did the following calculation to calculate the change in momentum:

The result is relatively close to what we got for the area under the force vs. time graph. Since the calculated change in momentum of the cart is almost equal to the measured impulse applied to the cart, we have verified the impulse-momentum theorem.

For the next part, we added 500 grams to the cart, for a total of 1141 grams, and ran the same procedure. Here are the graphs:

The graphs are shaped similarly to those of the first experiment. The area under the force vs. time graph is 0.8575 N*s. For our calculated change in momentum, we did the same calculation but instead using the initial velocity as -0.424 m/s and the final velocity as 0.359 m/s:

The result, 0.893 N*s, is also relatively close with the value of 0.8575 N*s from the area under the curve. Because of this, we can conclude that the impulse and change in momentum are equal to each other, despite using a cart with more mass, thus verifying the impulse-momentum theorem for this case. Something to notice about these two experiments is that the final velocities do not have the exact same magnitude of the initial velocities, and this could be due to an imperfect spring that does not produce a perfectly elastic collision. The recoil can only produce a nearly elastic collision, and this is a limitation of our equipment, rather than the procedure.

For the last part of the experiment is the test in the case of an inelastic collision. For this experiment, we used clay and attached it to a wooden pole, instead of using the upside down cart with the springy extension. We also replaced the rubber stopper extension on the cart itself with a nail, so the cart will stick to the clay when it collides. Other than those changes, the procedure is the same, and the mass of the cart is the same as the one in the first experiment, with 641 grams (we should have used the same mass as the second experiment, as it says in the instructions, so this is an error on our part). These are the resulting graphs:

The appearance of the graphs are quite different than what we observed in the last two experiments. It is expected that the velocity will eventually reach zero, which it did. However, in the force vs. time graph, there seems to be a negative force enacted on the cart, which makes sense because the collision is inelastic, so when the cart is trying to rebound out of the clay, the clay makes sure the cart sticks to it, so the force has to pull the force sensor when the cart is in the rebound phase, thus making the value negative. The value we got for the area under the force vs. time graph is 0.3154 N*s. The impulse is smaller than the one in the nearly elastic collision, which is to be expected, since the cart does not reverse the direction of its velocity, and instead remains at rest after the collision, thus making the value lower. For our calculated change in momentum, we used the same calculations but instead using the initial velocity as -0.483 m/s and the final velocity as 0 m/s:

The result is relatively the same as the measured impulse. This is promising, as we can now conclude that the impulse-momentum theorem is verified for inelastic collisions as well. Through these experiments, we verified the impulse-momentum theorem for both nearly elastic and inelastic collision, as well as testing what happens when we change the mass of the cart.

Conclusion: Some uncertainties that exist in the experiment are from the springy extension from the upside down cart. The spring is not perfect, and this makes the collision not perfectly elastic. This is seen in our data, since the final velocities do not have the same magnitudes as those of the initial velocities. It is also possible that the friction in the track could have contributed to the slight decrease in magnitude of the final velocities.

Overall, the experiment was a success, since we are able to observe that the values for the change in momentum and the impulse are relatively similar. We can conclude that the impulse-momentum theorem is applicable to both inelastic and elastic collisions, and we can confirm this by taking the area under the curve of the force vs. time graph and calculating the change in momentum and comparing the results.