Predict how far the cart will roll down the ramp

We place a cart of mass M on a ramp tilted at angle θ. It is attached to a spring of force constant k, which is initially at its rest length.

We hold the cart in the "start" position for a moment, then release it. The cart rolls down the ramp a distance L before coming to a momentary halt. It then starts back up the ramp, pulled by the spring. Ignore friction for the moment ...

1. What is the cart's kinetic energy at the moment it is released?
2. What is the cart's initial GPE, at top of ramp? A good reference location is its final position.
3. What is the cart's final GPE, relative to its final position?
4. What is the spring's initial SPE?
5. What is the spring's final SPE?
6. What is the cart's kinetic energy when it reaches the bottom of its motion?
7. Write an equation which gives the distance L in terms of other quantities (if there is no friction).

Okay, now let's add friction. Suppose that the coefficient of kinetic friction between track and cart is μ.

8. How much work is done by friction as the cart rolls?
9. Write an equation which gives the distance L in terms of other quantities (if there is friction).

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.