Daniel Guzman
Physics 4A.
Work kinetic energy theorem
The purpose of this experiment is particular experiment is to understand and prove that the change in kinetic energy of any system is equal to the total work done in the system.
Experimental procedure and apparatus description
Description of apparatus for experiment #1: The apparatus for this experiment consisted of a track, a motion sensor, a force sensor, a pulley a cart and a hanging mass. The apparatus in this experiment used two different sensors, a motion sensor that will record the position, and velocity as the car is moving, and a force sensor that will record the force that is being exerted on the cart by the tension on the string.
Experimental procedure for experiment #1 (work done by a conservative force) : The experimental procedure for this particular experiment was simple, yet at the same time very interesting due that different data is being collected at the same time, The procedure for this experiment consisted on setting up the apparatus correctly, which means to calibrate the force sensor correctly so it will read and record appropriate values for the force. Once the force sensor is calibrated one had to set up the apparatus by attaching a string to the cart and the hanging mass so the tension created in the string will make the car accelerate and move. Once this was set up the group was able to collect the desired data, which consisted of three graphs, one for force, one for position and the last one for velocity, once these graphs were collected we analyze the data and verify that the data collected was appropriate for the assumption of this experiment which is the work done on the cart by the tension force in the string should equal the kinetic energy gained by the cart.
Description of the apparatus for experiment #2 (work done by a non constant spring force) : The apparatus for this particular experiment consists of a spring, a motion sensor, a force sensor, a cart and a track. The set up for this experiment is very similar to the set up in the first experiment, the only thing that changes is that a spring is now used instead of the string a hanging mass used in the first experiment. In this experiment the force sensor was attached to a clamp and to the spring so it will record the force that the spring is exerting on the cart.
Experimental procedure for experiment #2: The experimental procedure for this particular experiment was quite simple. The procedure consisted on attaching the force sensor to a clamp that was placed at one end of the track, after the force sensor was put at the end of the track one attached the force sensor to the end of the spring and the other end was attached to the cart, once this is done one can proceed and stretch the spring by moving the cart, so some data force will be collected, once this data is collected we analyzed it and found the K constant of the spring, which is very important when finding the work done stretching the spring.
Description of the apparatus for experiment #3: The apparatus for this particular experiment is the same as the apparatus for the other experiment
Experimental Procedure #3: The experimental procedure for this experiment was quite simple, due that the set up was the same for the last two experiment. We started by stretching the spring, which is done by moving the cart forward, once the cart is moving forward one would start collecting date then when the cart reaches approximately 60 cm we let the car go so the spring would pullet it back and the data for the position and force of the cart would be recorded at the same time, which would allow one to have data for the position and the force at the same time. Once the data is collected one will find the area under the curve of the graph of force vs position, once this is done one can compare the kinetic energy at any position to the work done by the spring, so one can compare the work done by the spring to the change of kinetic energy of the system.
Data Collected
Graphs for each experiment
For this part of the experiment the area under the graph represents the work done by the constant force and if one was to compare the value obtained for the integral and the point at the end of the area of the integral one would find either that they are exactly the same or relatively close to each other, which lets one infer that the work is equal to the change of kinetic energy of the car.
This graph represents the same exactly relationship; nevertheless these graph was integrated over a longer interval the value for the integral is 0.1335 and value for the kinetic energy of the cart is 0.135, which is the same. This lets one infer that the change in kinetic energy is equal to work. because the values are exactly the same, which is amazing because by knowing the change in kinetic energy, one can find the work done.
For this part of the experiment one was asked to compare the value obtained for the area under the graph to a point at the end of the graph, what one would notice is that the values are relatively close, which once again holds true that the change in kinetic energy is equal to work, if one compares these two values by doing the percentage error one would find that the percentage error is 1.123% which is relatively small.
For Part # 2 the only thing that one had to find was the K constant for the spring this was found by graphing force vs position of the spring and by doing this one would be able to find the K for the spring because on would only have to calculate the slope of the graph in this case the K value was 3. 197, the other part that one had to find in this case was to calculate the work done in stretching the spring, which came out to be 0.5948 joules.
For the third part of the laboratory on had to find the change in kinetic energy of the cart after it is released from the initial position where the kinetic energy is zero, so the kinetic energy and the work had to be find in three different places.
In this case the integral gave 0.4343 ,which would represent the work and when one calculates the change in kinetic energy one would find that the two values matched perfectly , which once again proves that the change in kinetic energy is equal to work.
The same approach was used for this particular graph and once again it gave almost a perfect relationship which is good because the point of the lab was to prove that the change in kinetic energy is equal to work, for the third point picked in this part had a value for the work of 0.6054 joules and for the kinetic energy of 0.638
Part #4
In this part of the lab we watched a video and extracted the data from it, the pint of it was to confirm that the area under the graph was the same as the change of kinetic energy. in order words work equals the change in kinetic energy, in this case it was done by calculating the area under the graph an then calculating the change in kinetic energy to see it they were equal
Conclusion
In this particular lab the work energy theorem was proven or confirmed because every single relationship attempted showed that the change in kinetic energy is equal to the work done. multiple examples were tested and different experiments were done, and every single one of them held that the change in kinetic energy equals to work, the sources if uncertainty in this lab can come from overstretching the spring, which would change the results when comparing the work to the change in kinetic energy, another source of error can come from not calibrating the force sensor correctly, this would definitely alter the results because the work done on the system depends on the force, so it the force sensor does not read accurately the force, the area under the graph would not be the result that one would like to have. This lab was very interesting because my group and were able to collect good data and to prove that work energy theorem is true by using different approaches.
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