Lab 9: Conservation of Energy in a Mass-Spring System 10/6

Purpose

In this lab, we measured the kinetic energy (KE)  and gravitational potential energy (GPE) for the mass and spring, and elastic potential energy (EPE) for the spring to verify that energy is conserved through out the system.

Procedure + Lab Equipment

What we used:

• ring stand + clamp
• spring
• mass
• ruler
• logger pro 
• motion sensor + force sensor

This is the lab set up for when the spring is stretched, below is the motion senor

What we did: 

1.  we used the motion sensor to record the height of the spring when it was not stretched and when it was stretched
2. we attached the top end of the spring to the force sensor and hung the mass at the other end of the spring
3. we weighed the spring 
4. we then took the final reading as the mass was hung on the spring

Data

With logger pro, we were able to record the velocity of the spring as it moved

This is the height without and with the mass, and the mass of the spring is 0.044kg

The slope is the k constant of the spring

show integration work 

Calculations + Data Analysis

The data table that calculates KE, GPE, EPE, and Total Energy at each point as the spring oscillated from stretched to not stretched

This is the data table we created to find KE,  GPE, and EPE of the mass and spring at each point as the spring oscillated between stretched and not stretched. We then took those numbers and created a column for the total energy at each point. From the data table we see that the total energy through out the system appears to be consistent. 

From this graph we can see that when the spring is stretched, the total energy stays consistent, unlike when it bounces back up.

From this graph, we can actually see a clearer picture-that energy is consistent at every point as the spring goes from not stretched to stretched.

Summary

In this lab, we wanted to verify that in a mass-spring system, that the conservation of energy was true. We used logger pro to measure the velocity and position over a period of 10 seconds to help us find the energies at each point. Our graph showed that the energy was consistent throughout those 10 seconds, so, we were able to verify the conservation of energy in a mass-spring system.