05-Oct-2016: Lab 12 Conservation Of Energy - Mass Spring System

1. Title: Lab 12 Conservation Of Energy - Mass Spring System
    Name: Qiwen Ye (Sherry)
    Lab partners names: Jae Yoo, Chandler
    Date: 05-Oct-2016

2. Purpose
In this experiment, we was looking at the energy in the vertically-oscillating mass spring system in order to find the relationship between kinetic energy, gravity potential energy, elastic potential energy and position.

3. Introduction
Amuse the gravitational potential energy is zero at the groud, that we had a uniform spring whose top is held fixed at a height H above the ground. Then use calculus to show that the gravitation potential energy of the spring is mg(H+y)/2. Put our origin at the top of the spring and call downward the positive direction, assume that the spring has a length L, the top of the spring is held at rest but that the bottom end of the spring is moving at a speed v downward. The kinetic energy of the moving spring is 1/2(Mspring/3)v^2.

3. Apparatus/ Procedure
Set up the force sensor, motion sensor, clamps and spring as shown. Opened the LogPro to record the data. Mount the table clamp with a vertical rod to the table. Mount a horizontal rod to the vertical rod. Put a Force sensor on the horizontal rod with the loop of the sensor pointing downward. Then calibrate the force sensor using zero mass and a 1kg (9.8N) weight then remove the weight.

5. Measured Data

The mass of spring is m=89 g.

6. Graph by Prediction

7. Graph by LogPro

KE vs. GPE vs.EPE vs. Postion
Red: Gravitation Potential Energy
Blue: Elastic Potential Energy
Purple: Kinetic Energy
Green: Total Energy

KE vs. GPE vs.EPE vs. Velocity
Red: Gravitation Potential Energy
Blue: Elastic Potential Energy
Purple: Kinetic Energy

8. Conclusion
According to the graph above the GPE became lowest when the EPE of the spring was higher. Also, when the GPE became highest when the EPE of the spring was lowest. The reason was that when the string was fully stretched the mass would have every little gravitational potential energy. Even though the individual reading of graph have giant peaks, the overall sum was relatively staying steady. It shows that the energy is conserved. Some errors may in the accuracy of the reading of the spring constant measurement. And, the height may not be perfectly calibrated with the motion sensor or the spring itself was not perfectly.