Kevin Nguyen
Lab Partners:
Date of Lab Performed: 10 April 2017
Theory/ Introduction: The theory behind this lab was that we attempted to establish a relationship between work and kinetic energy. We did this by testing two ideas of physics: Work equals the change in kinetic energy and the integral of force equals to Work. In this lab, there were three experiments that tests these ideas (technically, there were four experiments, but the last experiment involved watching a video and collecting data from it).
In the first experiment, we used the force of tension force, a constant force, to measure the work done on a cart. We measured and graphed the tension force that was used to move the cart using Logger Pro. Then, we adjusted the force graph so that the graph would be a force (N) vs. position (m) graph, where force is on the y-axis and position is on the x-axis. We had done this because the area under the force vs position curve will give the work done on the cart. To find the change in kinetic energy of the cart, we made a new calculated column .5 * "mass" * "Velocity"^2 since this is the equation for finding kinetic energy. We then made a kinetic energy (J) vs time (s), where kinetic energy is on the y-axis and time is on the x-axis. This graph gave the kinetic energy of the cart at a given time. Ideally, the area under the force curve (from starting position) equals to the kinetic energy at that moment.
In the second experiment, we measured the work done by the non constant spring force. To do this, we had set up an apparatus that allowed us to test the force applied by the stretched spring vs distance the spring was stretched. We made a graph of Force vs Distance, where force is on the y-axis and distance is on the x-axis. After slowly and manually stretching out the spring, the graph formed on Logger Pro. Integrating that graph gave the work done by spring force. To find the spring constant of the spring, we used the idea that spring force equals to spring constant times displacement. The slope of the force line gave us the spring constant.
In the third experiment, we measured the work done by the non constant spring force and the kinetic energy of the cart in order to see if they are equal to each other at a certain point. We had set up an apparatus that allowed us to test the force of the spring and the kinetic energy of the cart. After collecting the data, we made two graphs, a force (y-axis) vs position (x-axis) graph and a kinetic energy (y-axis) vs position (x-axis) graph. Then we integrated the force vs position graph (from its starting position to whatever position we selected) in order to find the work done by the spring. We compared the work done by spring to the kinetic energy at the same final position and found that value of Work done by the spring was similar to the kinetic energy of the cart.
In the final "experiment", we copied the force vs position graph from the video and found the total area under the curve in order to find the total work done stretching the rubber band. Then we got the mass of the cart, change in position, and change in time in order to find the final kinetic energy of the cart attached to the machine. We then compared the kinetic energy to the work done on the rubber band.
Summary of experimental procedure
In the first experiment, we had up our apparatus like this.
The track is set up on the table. The motion sensor was at least 50 centimeters away from the starting position of the cart. A hanging mass of 500 grams was placed at the end of the string and a mass of 500 grams was placed on the cart. Before using the force sensor, we made sure to zero the force sensor and verified that it read 4.9 N when the hanging mass was at 500g and the cart was against the track stopper. The force sensor was then attached to the top of the cart. A track stopper was placed near the end of the track and a pulley was attached at the end of the track. To perform this experiment, a person held the cart at the starting position. Once the motion detector started clicking very fast, the person let go of the cart, allowing the cart to travel until it hit the stopper.
In the second experiment, we had set up our apparatus like this.
Again, the track was set up on the table with the motion sensor at least 50 centimeters away from the cart. The motion detector was set to "Reverse Direction" so that any direction towards the motion sensor was considered positive. The force sensor was attached to a metal rod at the end of the table. The force sensor was zeroed and calibrated with a force of 4.9N applied. A spring was attached to the force sensor and the cart. The cart was placed on the track. To perform this experiment, the person holding the cart would slowly bring the cart towards the motion detector once the motion detector began collecting the data.
In the third experiment, the same exact apparatus was used from the second experiment. The force sensor was zeroed. A kinetic energy vs position graph was set up along with a force vs position graph. The spring was stretched from its initial unstretched position to 0.6 meters. When the motion detector began collecting data, the person holding on to the cart let go of it.
In the fourth experiment, we watched a video titled "Work KE theorem cart and machine for Physics 1.mp4" We copied the graph shown in the video along with the data (mass of the cart, change in position, change in time) and solved for total work and kinetic energy. Then we compared the two results.
Table of Measured/ Calculated Data:
Experiment 1
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| Ignore the position vs time graph and the velocity vs time graph (top two graphs) |
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| Ignore the bottom two graphs. |
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| Ignore the bottom graph |
This picture shows how work and kinetic energy are calculated.
Conclusion
Experiment 1
Judging from the results from the graph, it seems that the value of work is almost equal to the change in kinetic energy.
Experiment 3
The work done on the cart is equal to the change in kinetic energy.
Potential energy of spring equals to Kinetic energy of the cart.
Experiment 4
The true kinetic energy of the cart is between 23.227 J and 24.373 J.
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