Work and kinetic energy in a system

Introduction:
According to the law of conservation of energy, we should be able to assume the change in work equals to the change in kinetic energy of an object. In this lab, we set up experiment to prove this assumption.

Apparatus:

We attached one end of a spring with force sensor and another end to a cart on an aluminium track, with motion sensor on another end of the track. With motion sensor and force sensor connect to the computer, we were able to get measurements of force and position relative to time, and we use them to calculate kinetic energy of the cart and the work done by the spring at any moment of our measurement. Then, we would be able to verify if the law of conservation was correct.










Data:
Before we collected any data, we calibrated the force sensor to be 0 N when the spring was at the rest.
To properly calculate the kinetic energy and the work done by the spring in the logger pro, we insert the following equation into logger pro:
Work done by spring= integral of ( force applied by the spring)
Kinetic energy of the cart= 1/2*m*v^2
The following are the screenshot of the graph along with the integral of force curve at different moment:

The integral of the curve showed that the work done by the spring was 0.5577 J.
The difference in kinetic energy was calculated to be 0.463J

The integral of the curve showed that the work done by the spring was 0.7350 J.
The difference in kinetic energy was calculated to be 0.653J

The integral of the curve showed that the work done by the spring was 0.8689 J.
The difference in kinetic energy was calculated to be 0.776J









Conclusion:
Compare the change in kinetic energy and work done by spring, we found the difference between them to be big in each different time interval. However, we found that their difference in each different time interval to be a close value. The reason it didn't seem to obey the law of conservation of energy was very likely to be caused by error in set-up. Because the spring we used was very old, it might no longer follow Hook's law, or there might also be an error when we try to calibrate the force sensor to 0.