The purpose of this lab is show the the conservation of energy. To do this we will need to measure 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 finally the total of all the energy.
Experiment:
To show the conservation of energy we will be using a mass attached to a spring. We will measure the springs natural length and the then measure the springs stretch to find the springs constant coefficient by using the formula mg = kx.
Now we use our motion sensor which is position on the floor to measure the distance the mass will oscillate up and down on the spring. We bring the mass to the springs natural length and let logger pro measure our time and distance which gives us velocity.
Here is a picture of the experiment setup:
Now that we have all our data collected from our motion sensor we had to calculate the six forms of energy we need to get the total energy on the system.
Here are the formulas we used to created calculated tables for each type of energy.
KE of mass : 1/2mv^2
PE of mass: mg * y
Elastic PE in spring: 1/2 K (stretch)^2
PE of spring: m(spring) / 2 * g * y + mgh/2 *h = height of top of spring and y = bottom of spring
KE of spring 1/2 m(spring)/3 * V^2(mass)
GPE: 1/2 m(spring) * g * y (y = bottom of mass height)
Then we where able to calculate the total energy in the system and graphed all this data on logger pro vs time.
At this point we realized the way we collected the data was wrong because we zero our motion sensors at the position of reset and reversed the position sensor so our distance would be positive going down. So we had to ask the professor for help to change our distance readings and we where calculate our data properly as shown in the graph below the top line is the conservation of of potential and kinetic energy in the system which creates an almost straight line.
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