6-Oct-2014: Coservation of energy of hanging mass on a spring

Purpose:
The purpose of the experiment conducted was to verify that energy is conserved in a mass spring system.

Apparatus:
The apparatus that was setup was a column with a force sensor attached to its end. Connected to the force sensor was a spring that suspended a mass at its end. A motion detector was placed directly below the spring to record its movement as see below:

Experiment:
We were asked to measure 5 pieces of data to help us prove the conservation of energy in the apparatus which are as follows:

1) KE of the mass
2) GPE of mass
3) Elastic PE in spring
4) GPE of spring
5) KE of spring

1) KE of mass

In order to find the kinetic energy of the mass we needed to find the velocity of the mass as it oscillated up and down the spring. In order to find the velocity we conducted the experiment and used the motion detector to find the velocity of the mass at small time intervals. By creating a new calculated column and using the equation for kinetic energy we typed the equation:

KE mass = (1/2) (mass) (velocity at any given time)^2

KE = (1/2) (0.05kg) V(t)^2

2) GPE of mass

Just as the kinetic energy of the mass we used the motion detector only to this time record the height of the mass as it oscillated. As the mass moved upward and downward the motion detector recorded the distance from itself to the mass. By finding the various heights we were able to create values for the gravitational potential energy of the mass as follows:

GPE mass = (mass)(gravitational acceleration)(height at time)

GPE = (0.05kg)(9.8m/s^2) h(t)

3) Elastic PE in spring

Once again using the motion detector we recorded the distance the spring extended or compressed. Before pulling the mass downward to cause the oscillation we had to calibrate the motion detector to zero when the mass hung on the spring at rest. Once done, we conducted the experiment and substituted the values found by the motion detector into the elastic potential energy equation:

PE elastic = (1/2) (spring constant) (distance spring moved)^2

In order to find the value of the spring constant we placed a mass of known value and hung it on the spring recording the distance the spring stretched. By substituting the values recorded in the equation for spring force we determine the following:

Force of spring = spring constant * distance 

(0.4 kg) (9.8 m/s^2) = spring constant (0.17 m)

spring constant = 23 kg/s^2

 Using this value we are able to substitute it into the gravitational potential energy equation:

PE = (1/2) (23 kg/s^2) (y(t))^2

4) GPE of spring and KE of Spring