Inclined Plane Calculator
Calculate forces, acceleration, and motion on inclined planes with friction
Calculate Inclined Plane Motion
Mass of the object
Incline angle from horizontal
Friction between surfaces
Vertical height of incline
Starting velocity down the incline
Physics Results
Force Components
Additional Info
Physics Analysis
Example: Block on Ramp
Problem Setup
Scenario: A 2 kg block on a 30° ramp with friction coefficient 0.2
Given: m = 2 kg, θ = 30°, f = 0.2, H = 5 m
Find: Acceleration, sliding time, and final velocity
Solution Steps
1. Gravitational force: Fg = mg = 2 × 9.807 = 19.614 N
2. Parallel component: Fi = Fg sin(30°) = 19.614 × 0.5 = 9.807 N
3. Normal component: Fn = Fg cos(30°) = 19.614 × 0.866 = 16.999 N
4. Friction force: Ff = f × Fn = 0.2 × 16.999 = 3.4 N
5. Net force: F = Fi - Ff = 9.807 - 3.4 = 6.407 N
6. Acceleration: a = F/m = 6.407/2 = 3.204 m/s²
Result: The block accelerates at 3.204 m/s² down the ramp
Real-World Examples
Gentle Ramp
Loading ramp
Steep Hill
Hiking trail
Frictionless Slide
Playground slide
High Friction
Rubber on concrete
Key Physics Concepts
Force Components
Weight splits into parallel and normal forces
Friction
Opposes motion, depends on normal force
Angle
Determines force distribution
Inertia
Affects rolling vs sliding motion
Essential Formulas
Parallel Force
F∥ = mg sin θ
Component down the slope
Normal Force
F⊥ = mg cos θ
Component into the slope
Friction Force
Ff = f × F⊥
Opposes motion
Net Acceleration
a = g(sin θ - f cos θ)
For sliding motion
Understanding Inclined Planes
What is an Inclined Plane?
An inclined plane is a flat surface that is tilted at an angle to the horizontal. It's one of the six simple machines that makes work easier by allowing us to apply a smaller force over a longer distance to move objects to a higher elevation.
Force Analysis
When an object rests on an inclined plane, its weight (mg) can be resolved into two components: one parallel to the incline (mg sin θ) and one perpendicular to it (mg cos θ). The parallel component tries to pull the object down the slope, while friction opposes this motion.
Motion Types
Sliding Motion
Objects slide when kinetic friction opposes motion
a = g(sin θ - f cos θ)
Rolling Motion
Round objects roll, considering rotational inertia
a = g sin θ / (1 + I/mr²)
No Motion
Static friction prevents motion when θ < tan⁻¹(f)
Critical angle determines motion
Real-World Applications
Transportation
Ramps, escalators, funicular railways
Construction
Roof slopes, wheelchair ramps
Tools
Wedges, screws, cutting tools
Recreation
Slides, ski slopes, skateboard ramps
Key Principles
Mechanical Advantage
Reduces force needed but increases distance
Energy Conservation
Potential energy converts to kinetic (minus friction loss)
Equilibrium
Balance between driving and resisting forces
Critical Angle
Minimum angle for motion to occur