Kinetic Energy of a Spring Cart

Purpose:
The purpose of the lab is to see if there is a correlation between a varying force applied over a distance and the kinetic energy of the object that is being acted on by the force.

Equipment Used:

The image is of a spring that is attached at one end to a force sensor and the other end to a cart with a block on top. At the other end of the track is a motion sensor. The force sensor will be used to measure the amount of force the spring is exerting on the cart and the motion sensor will measure the position and velocity of the cart. The point where the cart is attached to the spring's unstreched position will be the zero of the position graph. The direction towards the motion sensor is considered the positive direction.



Data Collected:

The cart was pulled towards the motion sensor and then released. The spring that was attached to the cart then exerts a force on the cart, accelerating it towards the define zero. Logger pro collected the force on the cart and position of the cart. The integral, or area under the curve, of the force graph should be equal to the amount of kinetic energy of the cart, which is half of the mass times the velocity^2.


Calculations:
When x = .193m the area under the curve was .4403 N*m and the kinetic energy is .346 J
When x = .153m the area under the curve was .5464 N*m and the kinetic energy is .433 J
When x = .110m the area under the curve was .6396 N*m and the kinetic energy is .501 J
The error at x = .193m was 21.4%
The error at x = .153m was 20.8%
The error at x = .110m was 21.7%

Conclusion:
There is a very high amount of error for every point at which data was collected, however the data is off by the same large margin for each point. This would mean that at some point during the experiment one aspect of the equipment was not properly calibrated. Perhaps the force sensor wasn't zeroed correctly or the position of the unstretched spring was not set to zero.

Sincerely,

Swaggy C