6th April 2015: Conservation of Energy Lab

Lab 11: Conservation of energy with a Spring

Purpose: The purpose of this lab is to essentially prove the theory of conservation of energy using a spring and a mass to show the oscillations of motion as a weight is applied to one end of the spring and a force sensor is calculating the energies as the move back and forth.

Spring constant = K

Procedure:  We first began by getting a spring, clamps, a motion sensor, force sensor, and a small mass. We use the clamps to attach a rod to our desk which went up some height and then an additional bar was used to clamp a pole above the spring so that a force sensor could be placed above the object and measure the forces. On the floor was motion sensor that was picking up the displacement of the object and spring as they oscillated. By knowing the total change in distance from the motions sensor and the force that the mass exerted on the spring we came up with a value of 14.86 for the spring constant of our mechanism.

This is a picture of what the mechanism looks like in class with the spring
hanging from the force sensor. 

After we found the spring constant we now need to find the forces of potential, kinetic, and total energies. By using the motion sensor for calculating the displacement and the force sensor to calculate the force, we were able to solve for our energies by inputting calculated columns into logger pro. 

Kinetic Energy (KE)= 1/2mv^2

Potential Energy mass (PE)= mgh

Spring PE= 1/2kx^2

KE spring= 1/2mv^2

PE gravity spring= mgh

Total Energy= Sum of (initial) KE+PE=PE+KE (final)

By inputing the formulas we came out with several data points that made up several energy curves as follows: 

These are all of the energies that we solved for
by using the different formulas we were given.

By solving for the calculated equations above we got the results from the energy graph in the picture above. With the groups knowledge of conservation of energy, we know that the potential energy of both the mass and the spring should be equivalent. We know that the have a relationship which they mirror each other meaning that if PE of the mass is increasing the PE of the spring should due decreasing and vise versa. In our data we notice that the graphs in fact do correspond with each other and total energy remains constant throughout our graph for the entire experiment. Since we found out the energies and matched those results to our predictions and knowledge of what we know we find that conservation of energy does support the spring and the mass. All in all our experiment was successful in proving conservation of energy within our system.