Procedure:
Experiment 1: For the first experiment we were to observe the work done by a non-constant spring force. We begin with a cart rigged to a spring connected to a force probe, which is on a track with a motion sensor set up on the other end of the track. Before collecting data we calibrated the force probe to 4.9 N applied and reversed the position of the motion sensor to get a positive slope on our graph. It is important that the motion sensor can read the cart's location so we rigged a flat panel to the cart to give it more area for the sensor to read. First we were to record the force applied by stretched spring vs. distance spring stretched and plot a graph of force vs. distance. Then we can find the work done by finding the area of the graph.
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| Lab apparatus with cart, spring, force probe, track, and motion sensor |
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| Cart attached to spring and force probe |
Now that our lab apparatus was completely set up, we opened the experiment file L11E2-2 (stretching spring) to display the force vs. position axes. Then we hit collect and slowly pulled the cart about 1 m towards the motion sensor, making sure to keep our hand out of the site of the sensor. Logger pro analyzed the data and plotted our graph below.
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| data set and graph of force vs. position. |
The slope of the graph gives us the spring constant, which came out to 3.045. Then using the integration routine in the program to find the area under the the graph gave us the work done, which came out to 0.6561 J.
Experiment 2: For the next experiment we used the same set up as the last experiment and measured the mass of the cart, which was .573 kg. We then created a new calculated column and entered an equation that would give us the KE of the cart at any point. The equation was KE=1/2*m*v^2. Again we make sure that the cart can be seen by the motion sensor. This time we begin collecting data when the cart is already stretched 1 m and then let go of the cart, allowing the spring to pull it back to an unstretched position. After a couple trials we got a good graph and saved it. The blue graph plotted was the force vs. position and we found the work done by using the same integration routine as the last experiment. The purple graph gives us the KE at any given position. We then analyzed the change in KE from initial position to 3 different final positions and compared those results to the work done by the spring up to those positions.
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| Work done = .2205, Change in KE= .236 |
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| Work done = .3141, Change in KE = .318 |
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| Work done = .3533, Change in KE = .36 |
After analyzing our data, we found that the work done on the cart was equal to the the change in KE for all three final positions. The work-energy theorem states that W=1/2*m*v^2final - 1/2*m*v^2initial. The equation verified our results.
Experiment 3: Part three of the lab required us to open up a movie file on the laptop entitled Work KE theorem cart and machine for Phys. 1.mp4. The video shows a professor using a machine to pull back on a large rubber band. The force being exerted on the rubber band is recorded by an analog force transducer onto a graph. Then the stretched rubber band is attached to a cart with known mass, so that when the cart is released it passes through two photogates at a given distance apart. The distance and the time interval between the front of the cart passing through the first photogate and then the second photogate gives us the necessary variables to solve for the final speed and the final KE of the cart. The force vs. position graph was plotted below in order to find the work done by the machine in stretching the rubber band.
By finding the area of smaller segments then adding them together, we were able to get a value for total work done at 25.675 J. Then solving for velocity using change in position over change in time and using the change in KE equation we were able to solve for KE, which came out to 23.88. Although the values are not exactly the same, we can say that the Work-Energy theorem holds true. There were a couple things that can create uncertainty in our final results such as the fact that we estimated the height and base of our graph to solve for the area. Also the video is pretty old so the equipment may not be extremely accurate.
Conclusion: After performing 3 separate experiments, we were able to verify that the work done was equal to the change in KE of the system. By finding the spring constant, measuring the area under the graph, and utilizing our KE equation, we were able to prove the work- KE theorem to be true.
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