7 October 2014: Conservation of Energy Lab 11

Objective:
The purpose of this lab was to study the conservation of energy and to understand that energy is transferred in different ways. To prove energy is conserved, the kinetic energy of the mass, kinetic energy of the spring, potential energy of the mass, potential energy of the spring, the elastic energy of in the spring, gravitational potential energy of the spring, and lastly the total of all the energy must be found.

Set up:

As you can see from this picture, we attached a spring to a set up made of rods and clamps that was high enough so that it could hang freely. We then attached known weights to the bottom of the spring. And lastly we had a motion detector on the ground to record oscillation and movement.












Procedure:
Before all else, certain data had to be collected:

Mass of Spring: 0.114 kg

Mass of Hanging Weight: 0.5 kg

Length of Spring Unstretched: 0.731 m

After these measurements were known, it would be easier to create a graphs using Logger Pro. We had to create a graph for  kinetic energy of the mass, kinetic energy of the spring, potential energy of the mass, potential energy of the spring, the elastic energy of in the spring, gravitational potential energy of the spring, and lastly the total of all the energy must be found. To calculate all these, we used the motion detector and Logger Pro to measure the velocity and position at certain times. However, finding some of the equations needed proved a bit trickier. Luckily, the professor helped us to find equations that would help us find all we needed. These is the help he provided: 

Here I have provided all the equations used in this lab:

Here are the equations (in order) for Kinetic Energy of the Mass, Potential Energy of the Mass, Elastic Energy of the Spring, Potential Energy of the Spring, Kinetic Energy of the Spring, and Total Energy.








As seen, in these equations, we must find k (spring constant of the spring) to find EE. To do this, we mounted the spring and mass to a force sensor and created a Force vs Position graph using Logger Pro. This is the graph that resulted. The slope of the graph is our k.

k=20.86

 Now that we knew everything that we needed to know, we created all our equations on Logger Pro that allowed us to create graphs of all our energies. The resultant graphs looked like this:

(Note (In order from bottom): Kinetic Energy of Mass= orange, Potential Energy of Mass= purple, Eleastic Energy of Spring= red, Kinetic Energy of Spring= blue, Potential Energy of Spring= green, Total Energy= yellow.

To prove that energy was conserved we must take a look at our the values of Total Energy (TE: dark puple):

As yo can see, the total energy was around 3.3-3.4 J with some but not drastic deviations. Here is a look at the total energy graph:

Conclusions:

Through the graph of Total Energy vs Time, it was apparent that energy was constant and conserved. Although there were slight fluctuations found in the table of Total Energy, the discrepancies were not drastic as they never were above 0.1 J. This means that no new energy entered the system and no energy left the system thus proving what we set out to prove: the principle of the conservation of energy.