Ramp and Rig
Resolve forces, examine limiting friction, balance a beam and keep a suspended sign safe. Gravity is 9.81 m/s².
Crate on a ramp
For three forces in equilibrium, the force arrows close into a triangle when drawn head-to-tail.
Resolved forces
Challenge
Set the apparatus, then press Check.
The physics
Slope: normal reaction N = mg cos θ. Down-slope weight component = mg sin θ. Limiting friction is μs N; kinetic friction is μk N. Acceleration while sliding = (mg sin θ − μk N)/m.
Strings: T₁ cos θ₁ = T₂ cos θ₂, and T₁ sin θ₁ + T₂ sin θ₂ = W. Angles are from the horizontal. The knot and strings are light.
Beam: a rigid beam in equilibrium has zero net moment about its pivot. The weight of the beam acts at its centre of gravity. A negative unknown downward load means an upward force is needed instead.