2 October 2014: Work- Kinetic Energy Theorem Lab 10

Objective:
The purpose of this lab is to find the relationship between work and kinetic energy. Our experiment aims to prove that the total amount of work is equal to the total kinetic energy at a certain position.

Materials:
1) a cart
2) a block
3) a spring
4) clamps and rods to secure a force sensor
5) a smooth track on which to push the cart
5) a force sensor
6) a motion sensor
7) Logger Pro

Set Up:

For this experiment, we placed a the cart on top of the track and the motion sensor at the end of the track. (The motion sensor will measure kinetic energy) We then placed a block on top of the cart, Lastly, we attached a spring to a force sensor secured with a set up made of clamps and rods.  (Force senor will measure the force of the spring.)










Procedure:

First we had to calibrate the force sensor using a hanging known mass. Next we pulled the cart along with the spring and zeroed the motion detector so that when we let go of the cart the motion detector would record positive distance and not a negative distance.

Since all the work done will be completed by the spring when it snaps back after being pulled, all the work will be done in a short amount of time. This is why it is important to collect data at 30 samples per second.

We also recorded the mass and the cart together which was 0.681 kg. This mass would allow us to create a kinetic energy graph. Finally we were able to proceed with our experiment

We stretched the spring by pulling the cart back, started recording data, and let go of the cart. Then we analyzed the data we collected.














Results:
After releasing the cart, Logger Pro was able to create a Force vs Position graph for us and we were able to create a Kinetic Energy vs Position graph manually. We then took the integral of the Force vs Position graph because that calculates work and compared it to the Kinetic Energy vs Position graph. The resultant graph looked like this: (Note: Kinetic Energy vs Position = purple, Force vs Position = blue)

As you can see from the graphs, the integral of the Force vs Position graph closely equals the value of the Kinetic Energy graph. This demonstrates what we set out to prove about the work- kinetic energy theorem. The work done by the spring equals the kinetic energy of the cart.

Conclusions:
Even though the values are never the exactly the same, they come very close to each other. There could have been some discrepancies which could account for the difference in values. However as seen by the following table, there was not that much error between both values.