Lab 12: Conservation of Energy – Mass Spring System

1.     Lab 12: Conservation of Energy – Mass Spring System

a.      Lab conducted by Mohammed Karim (author), Lynel, Andrew, and Richard.

2.     Objective –  Understand conservation of energy and the different forms of energy the system takes depending on position, height, speed, and force.

3.     Theory/Introduction – As if Physics wasn’t hard enough, we’ve decided to throw Calculus into it. One may ask themselves why? Well, because life is less than ideal. Not every mass is uniform and the gravitational potential energy is not always just mgh. As shown in figures 12.1 and 12.2, the calculations and derivations are done in detail to give us the equations we will be using. We need to keep in mind that in a hanging spring system, there are five forms of energy acting on it. There is gravitational potential energy of the hanging mass, kinetic energy of the hanging mass, elastic potential energy of the spring, gravitational potential energy of the spring, and kinetic energy of the spring. These values need to be kept in mind when we are conducting the following experiments.

4.     Apparatus/Procedure – Explain Apparatus and Procedure

           The apparatus above shows a spring hanging vertically with a mass tied onto it. There is a force sensor on top of the system, and on there is a motion sensor on the floor. With these, we will be detecting force and distance with respect to time. We then stretch the spring and allow it to oscillate, while running the various sensor to give us necessary data to plot a few graphs. After conducting the experiment, we plotted position, velocity, kinetic energy, gravitational potential energy, and elastic potential energy. (See Figures 12.3-12.6)

5.     Data Tables

Figure 12.1 - pt. 1/2 - Calculus required to find out energy equations with realistic conditions.

Figure 12.2 - pt. 2/2 - Calculus required to find out energy equations with realistic conditions.

Figure 12.3 Elastic potential energy vs. position and velocity graph. It shows the relation between position near equilibrium and potential energy.

Figure 12.4 Gravitational potential energy over position and velocity. GPE, being related directly with height, varies with position.

Figure 12.5 Kinetic Energy over position and velocity graphs. Shows the balance and how when velocity is zero, kinetic energy is and when velocity is at its peak, kinetic energy is as well.

Figure 12.6 - position over time and velocity over time graphs. The simple building blocks used to find the energy graphs.

6.     Conclusion – Conservation of energy is a very cool concept in the sense that it is very easy to follow. Energy is always in the system and is not lost (unless its due to heat or some other form). Therefore, if one energy is not present, the other form will have a lot more energy. This is shown in the graphs above. In the system, when it reaches the top or bottom, velocity is zero. Therefore, energy is zero, however, gravitational and magnetic potential are very high. When the object is at an equilibrium point, the velocity is at its highest, meaning kinetic energy is very high.