Acceleration Down an Incline with Friction
Worked example: 30° ramp with μk 0.2 → 3.2048 m/s² — press Try an example to run it live, then adjust anything.
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Sliding down →
Grade 12Grade 12 Physics
Down the incline →
UniversityEngineering Mechanics
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Acceleration Down an Incline with Friction explained
Gravity pulls the block down-slope with mg sin θ while friction drags back with μₖ mg cos θ; divide the difference by m and the mass drops out, leaving a = g(sin θ − μₖ cos θ). A 30° ramp with μₖ = 0.2 gives 9.80665 × (0.5 − 0.2 × 0.866) ≈ 3.20 m/s², a third slower than the frictionless 4.90 m/s². If the bracket comes out negative, the block was never sliding in the first place — the slope sits below the angle of repose, and the honest answer is a = 0.
Solving for θ uses the amplitude-phase identity sin θ − μ cos θ = √(1+μ²)·sin(θ − arctan μ), which is why the rearranged angle carries an arctan and an arcsin. The equation is the working model behind ski-slope grooming, luge run design and conveyor chute angles, all of which are chosen to land the acceleration in a narrow, controllable band.
Acceleration Down an Incline with Friction formula
- = Acceleration (m/s²)
- = Incline angle (°)
- = Coefficient of kinetic friction
Missing one of these? Work it out first, then come back
- Acceleration — Newton's Second Law, Final Velocity (Uniform Acceleration)
- Incline angle — Normal Force on an Incline (N = mg cos θ), Weight Component Along an Incline (mg sin θ)
- Coefficient of kinetic friction — Kinetic Friction Force (f = μₖN), Maximum Static Friction (f = μₛN)