Daniel Guzman
Physics 4A.
Lab 14: Impulse and momentum activity
Purpose of the experiment: The purpose of this particular experiment is to prove that the change on momentum of any body or object is equal to the impulse that the body experiences.
Apparatus description: The apparatus for this particular experiment consisted of a motion sensor, a force sensor, a track, a cart that had to different set ups, one of them with a stopper at one of its ends and the other one had a nail at one of its ends, a piece of clay was also used in this experiment.
First Set up
This is the initial set up the apparatus where the car is placed on a level track on which the motion sensor is at one of its ends and car on which the car on the track will collide.
This particular set up is for the elastic collision, this set up was the same set up as the past picture; however here is shown the position at which the stopper on the car should be placed for t to collide with the spring that is attached to the other cart.
This picture just as the last two pictures show the same exactly apparatus, yet in this picture is represented the collision.
Second set up
As mentioned before the cart will have two variations, one with a stopper at one if its ends and the other one will have a a nail attached to the force sensor. The second variation is used in this experiment due that an inelastic collision has to happen
This picture represents the second set up and the inelastic collision between the cart and the clay
Experimental Procedure
The experimental procedure of this experiment consisted on setting up first the correct apparatus due that the two collisions are totally different. In our lab group we first did the elastic collision; therefore, we used the cart that had the rubber stopper, so when it collides, the collision will be elastic. Once everything was set up we did a trial just to see if the stopper placed in the car will hit the target, after this was verified we proceeded and push the cart and hit collect data on the laptop so the initial and final velocity of the cart will be measured as well as the force that is measured by the force sensor that is in top of the cart. We measured the initial and final velocity so that we can calculate the initial and final momentum of the cart, having these two vectors one can find the change in momentum, which will give one the impulse. Also in this first experiment we measured the force using logger pro which give one the graph of the force vs time, from which one can also obtain the impulse that the cart experienced by integrated the area under the graph.
This graph shows the graph of velocity of the car from where we extracted the initial velocity of it, Nevertheless we used the graph of position vs time and determined the slope of it at a certain time, which let us determine the initial velocity of the cart.
This graph shows the graph of force vs time, from which one can get the impulse by integrating the area under the curve, This graph was obtained using the force sensor that was attached to the top of the cart.
Having the initial and final velocity of the cart and having the result of the integration will allow one to compare the impulse obtained using the change of momentum and the impulse obtained by integrating the area under the graph of force vs time.
The procedure for the second part of the lab was somehow simpler due that the collision is inelastic, which implies that the final velocity of the cart will be zero, so we did not have to measure the final velocity of the cart. In this part of the experiment we measured the initial velocity using the same approach as we used for the first part of the lab. Also we measured the force vs time because it will provide one the impulse that the cart experienced when one integrates the graph of position vs time. The approach taken in first part of the experiment was the same approach taken in the second part of the experiment.
Data Table and Calculations
The data collected is in red: impulse obtained from the integral of the graph, the initial velocity and final velocity obtained using the motion sensor and the mass of the cart which was obtained by using a scale.
Sample calculations
Conclusion
In this experiment one was trying to verify if the change in momentum that an object has would be equal to the impulse that the object would experience. From the data collected and the different calculations made one can conclude that the change in momentum indeed equal to the impulse that the object experiences. Nevertheless, the results obtained in this experiment were not as accurate as one would like them to be due that the percent errors for both the inelastic and elastic collisions were really big. For the elastic collision the percent error was 7.8% and for the inelastic collision the percent error was 20.8 %. When one analyzes these two percent errors one can assume that there are a lot of sources of error for this experiment. Some of the sources of error come from the apparatus used, for example the stopper in the cart might not collide perfectly with the spring in the cart, which bring uncertainty and error to the experiment and to the calculations. Another source of error for this experiment can come from the method used to measure the initial velocity of the cart due that for the second experiment the percent error calculation, which lets one infer that the measurement of the initial velocity of the cart was not measured correctly.
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