6-Oct.-14: Conservation of Energy

Purpose:

To verify the conservation of energy in a mass-spring system.



Apparatus:

Our set-up included -
a supported/hanging spring (m=0.064-kg),
a weight (m=0.300-kg), and
a motion detector

Things to measure: 

1. KE of mass (from motion sensor)
2. Gravitational PE of mass (measure the height above the sensor)
3. Elastic PE in spring - 1/2k(stretch^2)
   k - Hang mass. Get stretch Δy
4. Gravitational PE of spring
   -Find expression for GPE of the spring
   -Choose a representative bit of spring, with mass dm (piece of mass)
   The little bit of GPE it has is, d(GPE)=dmgy 
5. KE of spring
   - choose representative piece of mass dm

Experiment:

1. We first measured the spring constant, k, by measuring the distance between the bottom of the spring and the ground when there is no mass attached to the spring
   Next, we measure between the same points, but with a mass of 300-g attached to the spring.
   
   Using Hooke's Law : F=-kΔxwe find k=11.76-N/m
2. We then derived equations to calculate the Gravitational PE of the spring and the KE of the spring.
   
   
   ------------------------------------------------------------------------------------------------------------------
   
3. We pulled the mass, which was attached to the hanging spring, downward to give the spring a vertically oscillating motion and recorded the mass' position a certain time period which gave us the velocity needed for our calculations. (graph below)

After finding a way to calculate each energy in our apparatus -



- we graphed each with a calculated column in LoggerPro. We note that when calculating the total energy of the system through the graph, it closely resembles a straight, horizontal line. This shows that with some uncertainty, energy is conserved.





Conclusion:
The total energy is reasonably constant - this shows that the energy is conserved in our mass-spring system.

A Great Day for Physics.

(10/6/14 7:02 am)