8 April 2015- Work Energy-Theorem Lab

Lab 9: Work Energy-Theorem

Purpose: We examined the proven conjecture of the work-energy theorem that is equal to the kinetic energy graphs area under the curve which is the total work being done.


Procedure/Materials: In order to begin the experiment, we first began by using a metal track that lay across our desk which we placed a cart on and attached a spring to. At one end was the motion sensor which was calibrated to zero, on this same end the cart has a spring attached to the sensor that is unstretched but when we do stretch it the motion sensor will record the data. As soon as we calibrated our motion sensor we began the experiment which involved us pulling the cart back a certain distance. After doing so this distance was measured and then we began recording our data using logger pro. As we released the cart logger pro began measuring data on the force vs. time graph.

This is the force vs. time graph. 

This is a picture of the experiment we did in class to do the force vs. position graph. 

After recording the data we added another column in order to incorporate the calculated kinetic energy of the system deltaKE= .5mv^2. We then used this formula to compare and contrast the value of kinetic force vs time and the total kinetic energy vs time over that same exact time interval, there was some small error. We had to use three separate graphs to show the three different points we tested for each kinetic energy. 

Kinetic energy is .165 and the integral under the force vs time diagram is .152

Area under the curve .344 vs. kinetic energy of .365

area under the curve .453 vs. Kinetic energy .432

These three different intervals are the work energy theorem which is represented by force x time. The area of this integrated curve should be equal tot he kinetic energy with respect to time. As logger pro compared the two graphs we found that this relationship is hared between work energy theorem and kinetic energy, although we had an error. Our data was only of by 1 or 2 percent which could have easily occurred when the motion sensor was measuring data or not zeroing our equipment correctly, leading us to the conclusion that we had a successful lab in learning about the work energy theorem and its relationship with the area under the curve being equal to kinetic energy.