Inclined Plane Force Calculator
Resolve the weight of a mass on a ramp into its along-slope and normal components, add friction and find the net force and acceleration down the incline.
How it works
F_parallel = m·g·sin θ · Normal N = m·g·cos θ · Friction = μ·N · a = (m·g·sin θ − μ·m·g·cos θ) ÷ m
On a ramp the weight m·g splits into a component along the slope (m·g·sin θ) that tries to slide the block down, and a component pressing into the surface (m·g·cos θ) that sets the normal force. Kinetic friction opposes motion with magnitude μ·N. The block accelerates only when the along-slope pull exceeds the available friction; otherwise it stays put. Note the acceleration m·g·sin θ / m = g·sin θ is independent of mass on a frictionless ramp.
Worked example
A 10 kg block on a 30° ramp with μ = 0.2: weight = 98.1 N, along-slope = 98.1·sin30° = 49.05 N, normal = 98.1·cos30° = 84.96 N, friction = 0.2·84.96 = 16.99 N. Net = 49.05 − 16.99 = 32.06 N, so a = 3.21 m/s².
Sources: Inclined plane — Wikipedia
Frequently asked questions
Why does the normal force shrink as the ramp gets steeper?
The normal force balances only the component of weight perpendicular to the surface, m·g·cos θ. As θ increases, cos θ falls, so less of the weight presses into the ramp — and at 90° (a wall) the normal force is zero.
At what angle does the block start to slide?
It begins to slide when m·g·sin θ exceeds the maximum static friction μ·m·g·cos θ, i.e. when tan θ > μ. That threshold angle, arctan(μ), is called the angle of repose.
Does a heavier block slide faster?
No. On a frictionless ramp the acceleration is g·sin θ regardless of mass, and with friction it is g(sin θ − μ·cos θ) — mass cancels out in both cases.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.