To accomplish this goal we took a physics and mathematical type approach. What we did was to set-up a nearly elastic collision between two carts and measured the velocity, force, and time before and after the collision for different masses per experiment; we also did one experiment with a nearly inelastic collision with the heavier of the two masses that was used for the nearly elastic collision so we could try to prove the Impulse-Momentum theorem mentioned earlier is true. For example, we used the recorded data to calculate the area under the force vs. time graph during each trial with a tool that logger-pro has to obtain an Impulse value and then compared them to calculations for the change in momentum for the respective experiment with handwritten mathematical calculations to get a value for the change in momentum to compare and contrast the data. The velocity was measured with a motion sensor because we could get a distance vs. time graph and then use the application tool of logger pro to get a value for our velocity which is the slope of that graph. As for the set-up that we used, it was composed of one metal track, two metal carts, one force sensor, a digital balance, and a motion sensor. The force sensor was calibrated and the motion sensor was confirmed to be working before we got started with the experiments.
To begin with we set up the track, weighed the two carts, and calibrated the force sensor as well as the motion sensor. The track was a single metal track about one meter and a half long and about six inches wide; one of the carts had a spring attached to its front side and was attached in a horizontal manner to metal rods and clamps, and the other had the force sensor firmly attached to the roof of it with the actual force sensor facing the collision site to measure the collision force per each experiment. As for the motion sensor it was facing the rear of the cart with the force sensor attached to it, about thirty centimeters away. Then we opened up the logger pro computer application, gave the cart with a force sensor on its roof a push towards the one secured, measured the force, distance, and time per respective experiment so we could gather data necessary for the completion of the force vs. time graph as well as the distance vs. time graph for each experiment. Importantly, the nearly inelastic experiment was done differently then the first two because we took of the cart the was attached with the rods and clamps then placed a clamped piece of wood with clay on its front so the cart with the force sensor could hit the wood and get stuck when they collide. Also, the tip of the force sensor was changed from a rubber stopper type tip to one that had a sharp point so it can get stuck the impact site to get an inelastic type collision. For experiment one we used the mass of the cart only, and for experiment two and three we added five-hundred kilograms to the top on the cart with the force sensor on it. Next, for the calculated values of the impulse per each trail we used a tool the logger pro application program has that let us get a value for the area under the graph ( or integral ) that is the value for the impulse for each experiment. Lastly, the calculations for the change in momentum was done by hand because we had the mass of the cart and the value for the velocities before and after the collision for each experiment.
This is an image of the set-up for the first two experiments of the nearly elastic collisions. Notice the way that the cart was attached horizontally with the rods and the clamps. Also, note that the professor was calibrating the force sensor.
This image shows the third experiment for the nearly inelastic collision from the rear. Note the clay attached to the piece of wood instead of the horizontal cart with the rubber type tip.
This is the image taken of the graphs of the distance vs. time on top and the force vs. time graph on the bottom for experiment one.
This is the image taken of the graphs of the distance vs. time on top and the force vs. time graph on the bottom for experiment two.
This is the image taken of the graphs of the distance vs. time on top and the force vs. time graph on the bottom for experiment three. Note that the force vs. time graph looks different after the main area under the graph in contrast to experiment one and two. I think this may be due to the tip of the nail on the cart getting stuck to the wood or the clay on its way back after the impact.
In conclusion, the experimental values that we calculated were very similar in value hence the whole lab proved to show evidence that the Impulse and Momentum theorem is true. Of course, I do believe in the theorem because smarter men discovered it so regardless of the errors that we found in our total experiment does not deflect me from believing the theorem. Although, our errors were such a low value that I believe we did the experiment adequately well. The absolute difference for experiments one through three: 0.0116 N*s; 0.0055 N*s; 0.0182 N*s. As for the reason(s) for errors, I think one was that we didn't weigh the cart with the force sensor on top of it so that through the calculations of for change in momentum. That error would definitely cause a difference in the values of Impulse and Momentum. Otherwise, the force sensor may be a cause for error because it may of slightly malfunctioned during the trials. But, that error would be hard to prove. Interestingly, the force vs. time graph for the last experiment is different I believe because the nail got stuck to the wood or the clay so it pulled back on the force sensor causing a negative force that is seen after the main total force area of the experiment. Lastly, even though the values for Impulse and change in Momentum were not the same I think the theorem clearly presented itself because of the close precision between values.
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