4/08/15: Work-Kinetic Energy Theorem Lab 11

Purpose: By performing three different experiments, we are to determine how the work done on a cart by a spring compares to the change in kinetic energy of the cart. The work-kinetic energy theorem states that W = ∆KE.

Experiment 1
Apparatus:

The set up consists of a motion detector, track, force probe, spring, and cart.

We will be measuring the work done and spring constant when we stretch a spring through a measured distance. After setting up the apparatus, we made sure to calibrate the force sensor and to reverse the motion setting on the motion detector so the slope of our graph would be positive. We next opened the file called L11E-2 (Stretching Spring) to display a force vs. position axes. Once ready, we hit collect  and moved the cart slowly towards the motion detector until the spring stretch about 1.0 meters. Once logger pro generated our graph, we analyzed it and determined the spring constant is simply the slope of the force vs. position graph and the work done is the area under the force vs position graph.

We determined our spring constant k = 2.735 N/m and W = .4519 J

Experiment 2: We will be using the same set up, but the cart will be stretched a distance and the data will be collected once we let the cart go. Once logger pro generated our graph, we entered a formula in a new calculated column that would allow us to calculate the kinetic energy of the cart at any point. 

We are able to use the velocity vs time graph as well as the mass of our cart (.339 kg) to find the kinetic energy of the cart at any point. 

Once we had our calculated kinetic energy column, we then arranged the axes to read (kinetic energy and force) on the y-axis vs (position) on the x-axis. We used the integral fit on the force vs. position graph and compared it to the area under the kinetic energy vs. position graph. We analyzed the graph at three different section to make sure the work-kinetic energy theorem holds true and it certainly did.

Work done by spring = .3044 J and the ∆KE = .298 J

Work done by spring = .5326 J and ∆KE = .534 J

Work done by spring = .6354 J ∆KE =.638 J

This equation hold true. The work done by the spring is equal to the change in kinetic energy of the cart. 

Experiment 3: We were shown a video of a machine pulling back a large rubber band and the force exerted on the rubber band was recorded. It was then attached to a cart of known mass, stretched and released. The cart passes through two photogates, which are a known distance apart. The time it takes was also recorded. With the down distance and time, we can calculate the final speed of the cart and thus the final kinetic energy of the cart. 

Force vs. Position for the machine stretching the rubber band. 

By breaking the graph into various segments, we are able to calculate the work which was equal to 25.675 J. 

We then calculated the kinetic energy of the cart, which was equal to 23.8 J.

These values did not match exactly, but we still know the theorem holds true. 

Some possible errors for part 3 could be that since we estimated the heights and basses of our graphs, the end results will be slightly off and the equipment used in the experiment may not be as accurate as the equipment we are able to use today. 

Conclusion: By performing three experiments, we were able to determine a spring constant, analyze a force vs. position graph to find the work done from stretching the spring, verify that the work done by a spring is equal to the change in kinetic energy of a cart, and analyzed a video to further prove the work-kinetic energy theorem holds true.