Lab partners: Dylan, Chris
15 April, 2017
Work-Kinetic Energy Theorem Activity
Introduction: We performed four EXPTs to see how the theorem works: Work done by constant force, work done by a nonconstant spring force, kinetic energy and the work-kinetic energy, and lastly the work-KE theorem.
First EXPT: Work done by a Constant Force
1st. we set up a track, cart, motion detector, force probe, pulley, cart stop and hanging mass as shown in the picture
2nd. We zero the force sense. Then we verify that the force sensor reads 4.9N.
3rd. We added 500 grams onto our cart and entered this value as the mass. Our total mass of the cart is 1190g.
Cart mass: 545 g
force probe: 145 g
added mass: 500g
=1190g
Next, we hanged 50 grams onto the hanging mass, which will allow the cart to move. While it is moving, we collected data. We have created a Position/time graph, Velocity/time graph, and Force(N)/position graph for the cart moving at a constant speed. As the cart reaches the cart stop, the position will remain where it is at that point and the velocity will drop. On the third graph, the red line represents our Force/position analysis and the purple represents the kinetic energy.
In order to find kinetic energy, we went under the data menu, choose New Calculated column. Next we gave it a name: Kinetic Energy(KE) and units: J. The equation with be 0.5*mass*"Velocity"^2. After, we should get the results for kinetic energy(purple line).
Next, in the Force(N)/position graph, we highlighted a section of our graph from our leftmost position going to some distance to the right. We went to the Analyze menu and chose Integral to allow us to get a result(black letters)
We have tried two experiments: highlighting a smaller area of this graph and highlighting a larger area of this graph to see the difference.
For the smaller area, our integral value is 0.06N*M and for the kinetic energy of the cart is 0.07J. In conclusion, we can draw from our results that both values are relatively the same.
For the larger area, our integral value is 0.166N*M and for the kinetic energy of the cart is 0.156J. In conclusion, we can also draw from our results that both values are relatively the same.
The idea here is that work done on the cart by the tension force in a string should equal the kinetic energy gained by the cart at any point during the acceleration of the cart.
2nd EXPT: Work Done by a Nonconstant Spring Force
Now we measure the work done when we stretched a spring through a measured distance.
The model looks like the figure below.
We stretched the spring 0.6 meters from the starting point. Below is our Force(N)/Position(m) graph. From this graph, it gives us a slope of 3.460 N/m, which tells us the spring constant of our spring.
Next, I will display the Force vs distance graphs of both constant and nonconstant force.
First, we have the Force vs Distance graph of the constant force. By performing the integration routine, we are able to find the area under the graph of 0.5146 N*m
By knowing the spring constant of 3.46N/m, we are able to find the work by using the equation: 0.5kx^2, which will result in 0.662J. In comparison with the area 0.5146N*M and work 0.662J, they are relatively the same.
Next, we have the Force vs Distance graph of the nonconstant force. By performing the integration routine, we are able to find the area under the graph of -0.4021N*m . The reason for the results being negative because we verified that the motion detector is set to "Reverse Direction", so that toward the detector is the positive direction.
By knowing the work of the string 0.662J, we are able to compare that result with the integration result. In comparison with the area 0.4021N*m and 0.662J, they are relatively the same.
EXPT 3: Kinetic Energy And The Work-Kinetic Energy Principle
We used the same information from EXPT 2 in order to perform this. This time we will be finding the kinetic energy of the cart.
First to note that the cart's mass is 545 kg.
Under Data-> New Calculated Column, we entered a formula that would allow us to calculate the kinetic energy of the cart at any point.
Again, we stretched the spring for 0.6 m, then we released to collect data.
As a result, the kinetic energy reads 0.639 J and the integration(area under the curve) is -0.6583N*m. We are trying to prove that the kinetic energy equals to the area under the Force vs position graph. As a result, they are relative the same. Also, in comparison to the work done on the cart by the spring and the change in kinetic energy is relatively the same as well.
Since we know the formula Work=Fd, we can assume that the net work=net force*d. Since we know that net force=ma, we can replace "net force" with ma and the equation will be W=mad. I am assuming that the acceleration will be constant so I will be using a kinetic equation "Vf^2-Vo^2=2ad". In the equation, we can isolate the "ad", and the equation will be ad="(Vf^2-Vo^2)/2". Then we plug the ad in the equation "W=mad", Once plug it in we will have~
W=0.5m(Vf^2-Vo^2), which is kinetic energy.
EXPT 4: Work-KE theorem
We watched a movie filed entitled "Work KE theorem cart and machine for Phys 1.mp4. In the video, the professor pulls back on a large rubber band by using a machine. The force being exerted on the rubber band is recorded. Below is the Force/ Position graph for the machine stretching the rubber band in the video.
Below is the force vs position graph.
Below is the work done at each point and total work.
In conclusion, we were able to understand how the work-kinetic energy theorem works. We learned that values for the integral and the kinetic energy from EXPT 1 should have the same result. Same for EXPT 2 that the area under the graph should be equal to the work done by the applied force. Also for EXPT 3, we realized that kinetic energy should equal to the area under the Force vs Position graph. This lab gave us a better understanding of how the work-energy principle relates to kinetic energy.
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