Sliding down a ramp
The motion of a particle sliding (x metres) down a slope can be modelled using either Newtonian mechanics or Joule's law of conservation of energy. This file shows how these approaches both give a similar equation of motion for the particle.
What happens when the surface is smooth (that is, there is no friction)? (Set the coefficient of sliding friction at 0.) What happens when the slope angle is π/2 radians?