Presets
Playback
Ramp and crate
Run
Camera
Layers
Quality
Model check
The science
Forces along and across the ramp
For a ramp at angle θ, the weight mg splits into a part along the slope, mg sinθ, and a part pressing into it, mg cosθ. The ramp pushes back with the normal force N = mg cosθ. Friction opposes sliding and cannot exceed μN.
Will it slide? The crate stays put while static friction can balance the pull along the slope, that is while tanθ ≤ μs. Once it moves, friction drops to the kinetic value μk N, so the acceleration is a = g (sinθ - μk cosθ). The mass cancels out, so a heavy crate and a light one slide the same way; mass only changes the forces and the energy.
Speed and time. Starting from rest over a distance L: v = √(2 a L) and t = √(2 L / a). Energy check: the height lost, mg L sinθ, becomes motion plus friction heat, ½ m v² + μk m g cosθ L.
The oil patch. With the oil switched on, kinetic friction is halved after 55 % of the path, so the motion is two pieces with different accelerations; the second piece starts with the speed the first one reached.
Honest simplifications
The crate is a rigid block that cannot tip or rotate, friction is constant Coulomb friction per surface piece, there is no air resistance, and the run stops at the foot of the ramp. The 2D page drops the oil at a random moment of the run; here it is a fixed patch so the result can be predicted and checked. Crate size on screen grows with mass for visibility only.
Model checks (run live)
The default case against the 2D page's reference numbers; a time-stepped integration of the equation of motion against the closed form; the energy balance; and the angle where acceleration reaches zero against atan(μk).