INCLINE
Slides or holds? Friction renders its verdict before anything moves.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
A block of mass m rests on a ramp of angle θ with friction coefficient μ. Released from rest, does it slide the distance d to the bottom — and if so, how fast does it arrive?
Forces
Gravity pulls straight down, but the ramp only permits motion along its surface. Split the weight: W∥ = mg sinθ drives the slide; W⊥ = mg cosθ presses into the ramp, setting both N and the friction that resists.
Solve
The contest: tan θ against μ. Here gravity wins — the block slides. Friction fights at μN, leaving a = g(sinθ − μcosθ). Note that m cancels: a cannonball and a coin slide identically.
Slide
The block accelerates uniformly down the slope, friction gnawing at it the whole way. Distance grows as ½at², speed as at — the same kinematics as free fall, throttled by the surface.
Energy
At the bottom, the books must balance: the potential energy released splits between motion and heat. ΔPE = KE + Q — friction’s share is gone for good, scorched into the surface.