Lab 11 - Work-Kinetic Energy Theorem

 This is a sideways side-view of the setup that we had for this lab.

Purpose: The purpose of this lab is to prove that the work done by a stretched spring is equal to the kinetic energy that it generates.

Theory: We are trying to prove that work done by a system on an object is equal to the change in kinetic energy of the object.

Apparatus: Our apparatus for this lab was a metal coil spring approximately a foot long that does work by pulling inwards after it is elongated. We clamped a ring stand to the edge of the table, and attached the spring to the stand. We also placed a cart track in front of the stand-across the table. We then got a cart of mass 0.5439kg and attached a force sensor probe on top of it. The end of the force sensor was then attached to other end of the spring. We then used wooden blocks and track bumpers to get the spring to rest at the same height of the sensor. Using logger-pro, the force sensor, and a position sensor placed on the end farthest away from the ring stand on the track, we were able to calculate the spring constant which turned out to be 18.19N/m as shown on our graph below.

 Procedure: We then generated a new calculated column using the mass of the cart and "velocity" that is inputted into a new column by the position sensor. This new calculated column was the kinetic energy of the cart. We we generated the information for this new calculated column by measuring out how much we stretched the spring with the cart, then letting go of the cart so that the spring can do work on the cart and accelerate it. We then integrated to three different positions and compared the area under the curve (work) to the kinetic energy graph below it.

 Work= -1.029J
Kinetic Energy=  0.929J
~9% loss of energy

 Work = -1.975J
KE= 1.884J
~5% loss of energy

 Work = -2.733J
KE= 2.532J
~7% loss of energy

Conclusion: Based on our graphs and comparisons, it is safe to say that the work done by a spring on an object is equal to its change in kinetic energy. However, the amount of work done by the spring is NOT exactly equal to the change in kinetic energy  of the cart because energy is lost to many factors such as air resistance, and friction between the cart and the track. It was pretty cool to see that the work and the kinetic energy are very close to each other, meaning that our work-KE theorem is correct. The work done by a spring is equal to the change in kinetic energy of the cart, when all other factors are not accounted for.

My lab partner is Elliot Sandoval.