Case A Case B Gravitational PE Elastic PE Kinetic Energy Total Energy A mass is

Question

        Case A                   Case B Gravitational PE Elastic PE Kinetic Energy Total Energy A mass is connected to a spring and is hanging down at rest as shown in the figure at the right. The dotted line indicated where the spring would be at rest if no mass were connected to it. For the period of time we are considering (2.5 s), internal damping of the spring and air resistance can be ignored. We consider two cases: A- We pull the mass down by 10 cm and release it. B- We pull the mass down by 30 cm and release it. In the figures below are shown graphs of the y-position vs. time using the ruler as scale (but in unit of meters rather than cm), labeled A and B for our two cases. The eight graphs below were calculated on a spreadsheet and represent the gravitational potential energy, the elastic potential energy, the kinetic energy, and the total energy for each of the two cases. The units are Joules. Fill out the table by matching the graphs below with each of these quantities in these cases A and B. If none work, put 9.

Explanation / Answer

Gravitation PE: (both start from zero since they are pulled down)

Case A:5

Case B:6

Elastic potential energy,

Case A:1

Case B:8 (the spring achieves a position of no compression only in this case)

Kinetic Energy

Case A:3

Case B:4

Total energy:

Case A:7

Case B:2 (because this is extended more, it has more total energy since although the gravitational potential energy is lower, the elastic potential energy is much higher)

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