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A toy train comes off a hill traveling at a velocity v0, rolls down an incline of height h, rolls a short distance on a straight track, and strikes a bumper containing a spring, which is strong enough to stop the train. The distances are as indicated on the figure below. The train is just rolling, not powered.

Which of the graphs below could represent the following variables of the system expressed as a function of the position of the front end of the engine using the coordinate system shown? For this problem, ignore friction. Put the letter of all graphs that would work for a given variable in the space provided. If none works, put N and sketch what it would look like.

1. The total mechanical energy of the system.
2. The potential energy of the spring.
3. The gravitational potential energy of the train.
4. The kinetic energy of the train.
5. The x-component of the net force on the train.

Page last modified December 28, 2010: PE41