October 3, 2016: Work-Kinetic Energy Theorem Acitivity

Anthony Betancourt
Lab Partner: Josh Fofrich
Professor Wolf

Lab #11: Work-Kinetic Energy Theorem

Purpose:

The purpose of this lab activity is to introduce to the student a real world representation of the work-kinetic energy theorem.  The lab utilizes dynamics carts attached to a spring at one end and to a force sensor on the other.  Logger Pro will be utilized to get a visual representation of the kinetic energy and calculate the work done.

Procedure:  

Experiment 1

1. Set up a dynamics track and cart on your lab table along with the logger pro box and laptop designated to your lab group.
2. Attach a motion sensor on one end of the track, pointed toward the cart, and attach the force sensor on the other end utilizing a track bumper.
3. Attach a spring between the cart and the force sensor.
4. be sure to zero the force probe and motion detector with spring un-stretched.  
5. open experiment file "L11E2-2 (Stretching Spring)" to display force vs. position graph. 
6. to begin graphing, move the cart toward the motion sensor until the spring is stretched to 0.6m.
7. Find work done by using integration routine in the software. 

Experiment 2

1. Use same set up as procedure above. 
2. Under calculated column, enter a formula that will allow you to calculate kinetic energy of the cart.
3. Make sure x-axis is "position".   Zero force probe and motion detector and set position and force at the starting position.
4. To begin graphing, pull back the cart and release so that spring returns back to it natural position.  you might have to strike through data cells that don't showcase a smooth curved graph.

Theory:

In order to find the work done by stretching the spring we have to use the logger pro software to analyze the force vs. position graph and integrate the area under the graph which will tell us the work done.  In the second experiment, in order to find the change in kinetic energy after the cart is released the graph displaying KE vs. position needs to be under the Force vs. position graph in order to track the kinetic energy at a certain position.

Measured Data:

(Experiment 1; top graph shows force of spring on cart)

(Experiment 2; Top graph shows work done by the spring; bottom shows kinetic energy at 0.236J)

(Experiment 2; Larger area under graph for work done; bottom is KE at 0.557J)

(Experiment 2; larger area of work done; KE is 0.461 J)

Analysis:

The first graph shows the force of the spring on the cart while being stretched approximately 0.6m.  The slope of this graph is the force constant of the spring.  The work done is the area underneath the graph.  The second, third, and fourth graph all show the different amounts of work done and the amount of kinetic energy at the different positions.  

Conclusion:

The work done on the cart by the spring increases as the kinetic energy of the cart decreases.  This shows us that work done by the spring on the cart is inversely proportional to the kinetic energy in the system.  The work energy theorem states that all the work done on a system is equal to the change in its kinetic energy.  As the cart gains kinetic energy from the spring force, the change in that kinetic energy becomes more apparent than when it was at rest, thus, affecting the total amount of net work done on the cart.