Lab#11: Work-Kinetic Energy Theorem Activity
May Soe Moe
Lab Partners: Roya Bijanpour, Ian Lin
10-April-2017
Objective: To inspect and possibly confirm the statement of the Work-Kinetic Energy Theorem that the work done on a object is equal to the change in kinetic energy.
Introduction: We had done four separate experiments: (1) work done by a constant force, (2) work done by a non constant spring force, (3) kinetic energy and the work-kinetic energy principle, and (4) work-KE theorem. In this lab we wanted to confirm the Work-Kinetic Energy Theorem, which states that the total work done on an object is equal to the change in kinetic energy. We also knew that the area under the force vs. position graph is equal to work done on an object. Therefore, in this lab, we set up our apparatus so that we could get a graph of force vs. position graph, which would give us the work done on an object by finding an integrated value of an area under the graph and the kinetic energy at that position. When the two values we got from the kinetic energy and the integrated value of the graph are equal, we would compare them and see what we can conclude from our results.
Experimental Procedure:
Experiment 1: Work Done by a Constant Force
Apparatus:
(3) After the setup and leveling, we would calibrate the force sensor by just vertically holding the force sensor at first and set it to zero. And then we would vertically attach the 500 grams mass to the force sensor and set it to 4.9 N. After it was done, if the force sensor described the force or the weight of the mass to be around 4.9 N, we know that the force sensor is calibrated and it is good to go on with the lab.
(4) We added 500 grams to the cart, hanged 50 grams to the end of the string and pull the cart back.
(5) After that we released the cart, started to collect data, and plotted force vs. position graph.
(6) After getting the force vs. position graph, we added a new calculated column for kinetic energy to our table in Logger Pro and added our equation of kinetic energy- KE= 0.5mv^2, where our mass here is 1.177 kg.
(7) Once we got all of this, we integrated the area under the force vs. position graph using Logger Pro to give us the work done on the cart and kinetic energy at the same point.
(8) Above is how our graph came out. In our first graph, we highlighted a smaller area and determined the integral value (0.1287 Nm) and Kinetic energy (0.109J). In our second graph, we highlighted a larger area. Our value of work done on an object was 0.1775 Nm and the kinetic energy was 0.150 J.
(9) When we compared the two values: the integrated value of the area under the force vs. position graph and the kinetic energy from the graph at the same point, we saw that the two values were off by 0.0197 in the first graph and 0.0275 in the second graph. Although we repeated the experiment a few times, we got similar results. Therefore, we suspected that there was friction along the track, and part of the errors might be due to the force sensor, which we had to calibrate after every trial because we saw different force readings.
Experiment 2: Work Done by a Non-constant Spring Force
Apparatus:
(1) We set up our apparatus as above by attaching the spring to the cart and the force sensor while setting the motion detector on the other side of the cart and the force sensor. We made sure the track was leveled after the setup.
(2) We calibrated the force sensor by repeating the steps we did in experiment 1.
(3) We pulled the cart toward the motion detector until the spring is stretched about 0.6 m.
(4) Then we started collecting data for force applied by a stretched spring for 0.6m of distance.
(5) We began graphing the force vs. position graph as we pulled the cart.
(6) Once we got the graph, we integrated the area under the force vs. position graph.
(7) The integrated value from the force vs. position graph is the work done on the cart by a spring force, which came out to be 0.2424 Nm. The spring constant of our spring is the slope of the equation Force=mx+b. It also makes sense that our spring force equation is F=kx. Therefore, the spring constant is 3.511N/m.
Experiment 3: Kinetic Energy and the Work-Kinetic Energy Theorem
Apparatus:
Our apparatus for experiment 3 was set up the same as in experiment 2.
(1) We measured the mass of the cart, which was 0.549 kg.
(2) We added a new calculated column for kinetic energy of the cart. The equation for kinetic energy of the cart KE=0.5mv^2 was put into the Logger Pro to calculate kinetic energy at different points. Here, our mass was 0.549 kg, the mass of the cart.
(3) We calibrated the force sensor again by repeating the steps in experiment 1 and 2.
(4) After calibration, we pulled the cart along the track so that the spring was stretched about 0.6m from its natural length position.
(5) We began graphing when we released the cart and the spring pulled back the cart to its natural length position.
(6) We would then find the work done by the spring force for the displacement of the cart between any two positions by finding the area under the curve between two points. We would also calculate the kinetic energy of the cart be finding directly from the Kinetic Energy Versus Position graph.
(7) For the change in kinetic energy of the cart, we found the kinetic energy between the same two points we used to find for the work done by the spring force.
(8) We calculated the work done by the spring and kinetic energy of the cart at different positions and repeated a few times.
(9) Below is the calculated value of change in kinetic energy and the integrated value of the area under the graph-- work done.
Conclusion: From the first two rows, we can see that the work done between 0.155m and 0.222m and change in kinetic energy between that two positions are off by 26.9%. The second set was off by 13.9%, and the third set was off by 3.38%. According to the work-energy principle, the total work done by the spring on the cart is equal to the change in kinetic energy. The work done and change in kinetic energy are not quite close to each other. We speculated that there was some friction between the cart and the track. The force sensor was not functioning well, which might cause the different reading on the graph, because we had to calibrate it after each trial due to incorrect readings. Other factor that might cause error in our experiment was that the level is not leveled since the cart's velocity moved the track every trial.
Experiment 4: Work- KE Theorem
For this experiment, we watched the movie Work KE theorem cart and machine for Physics 1.mp4 in class. In this video, the rubber band was pulled back by using a machine and the force exerted on the rubber band was recorded by an analog force transducer onto a graph. The graph produced was as below. We calculated the total work done by the machine in stretching the rubber band by dividing up the graph into a triangle, trapezoids, and rectangles, and finding the areas under those shapes. We added all of the areas to get total work done.
The total work done calculated from the Force vs. Position graph was 22.3 J. The final kinetic energy of the cart attached to the machine was calculated to be 23.8 J by using the data from the video.
Conclusion: From our all four parts of the lab, we saw that there were quite difference in between the work done and change in kinetic energy. We doubted that this difference was due to the possible friction between the track and the cart, and the unreliability of the force sensor. Despite of our numerous trials of each experiment, we got our best datas within 20 % range. Therefore, in our results and datas, the work done and the change in kinetic energy are not quite equal to each other. If we had a better reliable apparatus, we might have gotten better results. We can say that since other groups' datas turned out that the work done and change in kinetic energy were pretty close unlike ours.
May Soe Moe
Lab Partners: Roya Bijanpour, Ian Lin
10-April-2017
Objective: To inspect and possibly confirm the statement of the Work-Kinetic Energy Theorem that the work done on a object is equal to the change in kinetic energy.
Introduction: We had done four separate experiments: (1) work done by a constant force, (2) work done by a non constant spring force, (3) kinetic energy and the work-kinetic energy principle, and (4) work-KE theorem. In this lab we wanted to confirm the Work-Kinetic Energy Theorem, which states that the total work done on an object is equal to the change in kinetic energy. We also knew that the area under the force vs. position graph is equal to work done on an object. Therefore, in this lab, we set up our apparatus so that we could get a graph of force vs. position graph, which would give us the work done on an object by finding an integrated value of an area under the graph and the kinetic energy at that position. When the two values we got from the kinetic energy and the integrated value of the graph are equal, we would compare them and see what we can conclude from our results.
Experimental Procedure:
Experiment 1: Work Done by a Constant Force
Apparatus:
 |
| The apparatus for first experiment: the string was not very visible in the picture. |
(1) We set up our apparatus as above: we used a cart connected with a hanging mass with a string through a pulley.
(2) Then we made sure the track was leveled, meaning the cart would roll along the track at a constant speed after giving a gentle push.
 |
| Leveling the Track |
 |
| Our total mass of the cart and 500 grams-- We put in this mass in our kinetic energy in the table. |
(3) After the setup and leveling, we would calibrate the force sensor by just vertically holding the force sensor at first and set it to zero. And then we would vertically attach the 500 grams mass to the force sensor and set it to 4.9 N. After it was done, if the force sensor described the force or the weight of the mass to be around 4.9 N, we know that the force sensor is calibrated and it is good to go on with the lab.
(4) We added 500 grams to the cart, hanged 50 grams to the end of the string and pull the cart back.
(5) After that we released the cart, started to collect data, and plotted force vs. position graph.
(6) After getting the force vs. position graph, we added a new calculated column for kinetic energy to our table in Logger Pro and added our equation of kinetic energy- KE= 0.5mv^2, where our mass here is 1.177 kg.
(7) Once we got all of this, we integrated the area under the force vs. position graph using Logger Pro to give us the work done on the cart and kinetic energy at the same point.
 |
| Getting the integral and Kinetic energy by highlighting a smaller area |
 |
| Our Graph of Force vs. Position graph with integrated value and kinetic energy: Larger area highlighted |
(8) Above is how our graph came out. In our first graph, we highlighted a smaller area and determined the integral value (0.1287 Nm) and Kinetic energy (0.109J). In our second graph, we highlighted a larger area. Our value of work done on an object was 0.1775 Nm and the kinetic energy was 0.150 J.
(9) When we compared the two values: the integrated value of the area under the force vs. position graph and the kinetic energy from the graph at the same point, we saw that the two values were off by 0.0197 in the first graph and 0.0275 in the second graph. Although we repeated the experiment a few times, we got similar results. Therefore, we suspected that there was friction along the track, and part of the errors might be due to the force sensor, which we had to calibrate after every trial because we saw different force readings.
Experiment 2: Work Done by a Non-constant Spring Force
Apparatus:
 |
| Apparatus of Experiment 2 |
(2) We calibrated the force sensor by repeating the steps we did in experiment 1.
(3) We pulled the cart toward the motion detector until the spring is stretched about 0.6 m.
(4) Then we started collecting data for force applied by a stretched spring for 0.6m of distance.
(5) We began graphing the force vs. position graph as we pulled the cart.
(6) Once we got the graph, we integrated the area under the force vs. position graph.
 |
| Experiment 2: Work Done by a Non-constant Spring Force= the Area under the graph. |
Experiment 3: Kinetic Energy and the Work-Kinetic Energy Theorem
Apparatus:
Our apparatus for experiment 3 was set up the same as in experiment 2.
(1) We measured the mass of the cart, which was 0.549 kg.
(2) We added a new calculated column for kinetic energy of the cart. The equation for kinetic energy of the cart KE=0.5mv^2 was put into the Logger Pro to calculate kinetic energy at different points. Here, our mass was 0.549 kg, the mass of the cart.
(3) We calibrated the force sensor again by repeating the steps in experiment 1 and 2.
(4) After calibration, we pulled the cart along the track so that the spring was stretched about 0.6m from its natural length position.
(5) We began graphing when we released the cart and the spring pulled back the cart to its natural length position.
(6) We would then find the work done by the spring force for the displacement of the cart between any two positions by finding the area under the curve between two points. We would also calculate the kinetic energy of the cart be finding directly from the Kinetic Energy Versus Position graph.
(7) For the change in kinetic energy of the cart, we found the kinetic energy between the same two points we used to find for the work done by the spring force.
(8) We calculated the work done by the spring and kinetic energy of the cart at different positions and repeated a few times.
 |
| Kinetic Energy at starting point for this area under the graph |
 |
| Kinetic Energy at end point for this area under the graph |
(9) Below is the calculated value of change in kinetic energy and the integrated value of the area under the graph-- work done.
Conclusion: From the first two rows, we can see that the work done between 0.155m and 0.222m and change in kinetic energy between that two positions are off by 26.9%. The second set was off by 13.9%, and the third set was off by 3.38%. According to the work-energy principle, the total work done by the spring on the cart is equal to the change in kinetic energy. The work done and change in kinetic energy are not quite close to each other. We speculated that there was some friction between the cart and the track. The force sensor was not functioning well, which might cause the different reading on the graph, because we had to calibrate it after each trial due to incorrect readings. Other factor that might cause error in our experiment was that the level is not leveled since the cart's velocity moved the track every trial.
Experiment 4: Work- KE Theorem
For this experiment, we watched the movie Work KE theorem cart and machine for Physics 1.mp4 in class. In this video, the rubber band was pulled back by using a machine and the force exerted on the rubber band was recorded by an analog force transducer onto a graph. The graph produced was as below. We calculated the total work done by the machine in stretching the rubber band by dividing up the graph into a triangle, trapezoids, and rectangles, and finding the areas under those shapes. We added all of the areas to get total work done.
 |
| The graph produced in the video |
 |
| The values of displacement, time, mass of the cart are from the video. The velocity and kinetic energy of the cart are calculated. |
Conclusion: From our all four parts of the lab, we saw that there were quite difference in between the work done and change in kinetic energy. We doubted that this difference was due to the possible friction between the track and the cart, and the unreliability of the force sensor. Despite of our numerous trials of each experiment, we got our best datas within 20 % range. Therefore, in our results and datas, the work done and the change in kinetic energy are not quite equal to each other. If we had a better reliable apparatus, we might have gotten better results. We can say that since other groups' datas turned out that the work done and change in kinetic energy were pretty close unlike ours.
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