10.1

Conservation of Energy in a Spring-Mass System

Student Notes

Run the simulation with the default mass and velocity. Note the motion of the ball, and the shape of the position vs. time graph.
Questions:

1. | From the graph of the ball's position as a function of time, sketch a graph of the ball's gravitational energy vs. time. Use the coordinate system shown on the screen.
2. | From the graph of the ball's position vs. time, sketch a graph of the ball's velocity vs. time.
3. | From the velocity graph, sketch the ball's kinetic energy vs. time graph.
4. | At the start of the simulation the spring is unstretched. Sketch a graph of the potential energy stored in the spring as it is stretched and compressed.
5. | If there are no forces acting on the ball other than the spring and the earth's gravity, sketch a graph of the sum of the ball's kinetic energy, the ball's gravitational potential energy, and the spring's potential energy.

After making each energy graph sketch, check your prediction against the appropriate graph by clicking on the graph legend for that energy.

1. | How will the graphs change if the ball has an initial downward velocity when the simulation starts?
2. | How will the graphs change if the ball's mass is doubled?

After making each prediction, make the change in initial conditions and compare your prediction to the simulation.

Self-test

1. | How would the graph of gravitational potential energy change if you used a coordinate system with an origin 1 m lower than the one used in the simulation?
2. | How would the energy graphs change if air resistance slowly removed mechanical energy from the ball and spring system?
3. | Why is the graph of the spring potential energy not sinusoidal?

Copyright © 2006 John Wiley & Sons, Inc. All rights reserved.