A cube starts from height h on a frictionless ramp, then slides on a horizontal floor with friction μ. Find the stopping distance d on the floor.
This interactive 3D physics simulation demonstrates conservation of mechanical energy and the work-energy principle. A cube slides down a frictionless ramp, converts gravitational potential energy into kinetic energy, and then slows down on a rough horizontal surface due to friction.
At the top of the ramp, the cube has gravitational potential energy. If the ramp is frictionless, this energy becomes kinetic energy at the bottom.
On the rough horizontal floor, friction does negative work and brings the cube to rest.
Using energy conservation and the work-energy principle:
Gravitational potential energy changes into kinetic energy as the cube slides down the frictionless ramp.
On the rough floor, friction removes mechanical energy and brings the cube to rest.
The stopping distance does not depend on the mass of the cube because mass appears in both gravitational energy and friction work.
A larger coefficient of friction gives a shorter stopping distance, while a smaller coefficient gives a longer stopping distance.
Conservation of energy means energy can change form, but the total energy remains constant if no external non-conservative work is done.
The work-energy principle states that the net work done on an object equals the change in its kinetic energy.
The cube stops because friction does negative work and removes its kinetic energy.
For height h = 10 m and μ = 0.8, the distance is d = h / μ = 10 / 0.8 = 12.5 m.