Consider the gravitational potential, kinetic, and total mechanical energies of a cart moving down an inclined ramp. (Also, let gravitational potential energy be defined to be zero when the cart is at the bottom of the ramp.

Question

A. Write an expression for the gravitational potential energy of the cart in terms of its mass M, the distance along the inclined ramp X, and the angle of the ramp THETA.

B. How will the kinetic energy, gravitational potential energy, and total mechanical energy change as the cart rolls down the inclined ramp. (for each type, does it increase, decrease, or stay the same)?

Answer 1

height = x sin theta

potential energy = m g h
= m g x sin theta
assuming x is zero at the bottom and positive up ramp

potential energy + kinetic energy = total energy = constant if ignoring friction

potential = m g x sin theta
kinetic = (1/2) m v^2
sum is constant so
as x gets small (going down ramp potential goes down)
v^2 has to get big