Lab 12 - Conservation of Energy of a Mass-Spring System

 

This is also a sideways view of the setup that we had for this lab. The spring was hung off of the force sensor, with a motion sensor at the bottom.

Purpose: The purpose of this lab is to show how energy is conserved in a mass-spring system.
Theory: The theory behind this is that energy is always conserved within a system. The only time when energy is not conserved is when there is an outside source that absorbs energy, or when it is converted into heat.
Apparatus: The apparatus uses most of the same components from the previous lab involving the cart, and spring. We used the ring stand and used it to extend a rod over the edge of the desk in a horizontal fashion. We then hung the spring off the rod, and hung a mass off the lower end of the spring. On the bottom of the hanging mass we taped an index card so that the position sensor that was directly below it could register its position more easily. We then used a laptop to retrieve all of our data.

Procedure: After we had everything set up, we then pulled on the mass a little bit and let it go. This then caused the spring and mass to oscillate up and down. The motion of the spring and mass was then recorded and used in the laptop. Using the data we collected we then created multiple calculated columns including "elastic potential energy", "kinetic energy", and "gravitational potential energy".

The graph below is KE vs. Position, it shows that as the mass and spring oscillate, the most kinetic energy it has is as it passes through the "natural" resting position of the system. This means that at the point that the mass was, before we pulled on the it, is the point where KE is greatest.

 

 The graph below is KE vs. Velocity. What this graph is showing is that where the velocity was zero, was where the KE was zero. These points occurred at the top and bottom turning points of the mass. This also shows that the KE was greatest at the points where the velocity was the greatest, which was at the "natural" resting position.

The graph below is of Gravitational PE vs. position. What this graph demonstrates is that the point with the greatest GPE is the point furthest away from the motion sensor, which also happens to be the highest point that the mass reaches.

 The graph below is GPE vs. velocity. This graph shows the oscillation of the system. This is shown because although at the bottom there is no more KE because the velocity is zero, and there is zero GPE, the velocity increases again.

 The graph below shows Elastic PE vs. position. What it demonstrates is that the position that is closest to the position sensor is the point with the most  EPE, and that at the highest position of the mass is where the EPE is the smallest.

The graph below shows EPE vs. velocity. What is really being shown here is the oscillation of the mass-spring system.

 These are all of the graphs put together into the y-axis, while the position is on the x-axis. This helps to demonstrate how the spring and mass are able to oscillate. This is because as the EPE loses energy, the GPE gains energy, and vise versa.

The graph above has the same y-axis, while the x-axis has been changed to time. This graph helps to even further illustrate how each energy is transformed into a different one.

Conclusion: It is pretty neat to see real world data provide evidence for things that I have known for years, but only from lecture and from accepting the fact that what I was taught was true. We created our own data and showed the various energies contained within a mass-spring system. We did not position the graphs in a way that made it seem like one energy was converted into another, they just happened. Every position on each graph is placed on the exact second(referring to time) as the others. As you can see from the graph above, the point on the graph where the kinetic energy is at its highest point is where the EPE and GPE are equal, or at their intersection points if the graphs of EPE and GPE were laid on top of each other.

My lab partner is Elliot Sandoval.