Inclined Plane with Friction Calculator
Enter mass, incline angle, friction coefficient and gravity to compute the acceleration, force components and whether the block slides.
Input Data
Results
At a glance:On an incline of angle θ, an object's weight mg resolves into a component mg·sinθ parallel to the slope (pulling it down) and mg·cosθ perpendicular (the normal force N). The maximum static friction is f_s,max = μ_s·N; if mg·sinθ ≤ f_s,max the block stays at rest. Once sliding, kinetic friction f_k = μ_k·N opposes motion, and the net down-slope force is mg·sinθ − f_k, giving acceleration a = g·(sinθ − μ_k·cosθ). If the bracket is negative the block decelerates (or cannot start upward). This tool reports the components, max static friction, net force and whether it slides, for a given μ (treated as kinetic once moving).
Formula
Down-slope: mg·sinθ
Normal: N = mg·cosθ
Friction: f = μ·N
a = g·(sinθ − μ·cosθ)
$$a = g(\sin\theta - \mu\cos\theta)$$$$N = mg\cos\theta, \quad f_{max} = \mu N$$$$\mu \geq \tan\theta \Rightarrow a = 0$$How to Use
- Enter mass m, angle θ (°), friction coefficient μ and gravity g.
- The calculator returns a, force components, max static friction, net force and sliding status.
Case Studies
Box on a ramp
m = 10 kg, θ = 30°, μ = 0.2, g = 9.81.
mg·sinθ = 49.05 N, N = 84.96 N, f = 17.0 N.
Net = 32.05 N down, a = 3.2 m/s².
FAQ
When does the block not slide?
When the down-slope component mg·sinθ is ≤ μ_s·mg·cosθ, i.e. tanθ ≤ μ_s. The critical angle (where it just starts) is θ_c = arctan(μ_s).
Does mass affect the acceleration?
No — mass cancels in a = g(sinθ − μcosθ), so all objects (regardless of mass) accelerate the same on the same incline with the same μ, like Galileo's finding without friction.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.