CalcHab

Online Inclined Plane Calculator

Analyze object motion along an inclined slope. Compute acceleration, normal force, parallel gravitational force, and kinetic friction coefficients.

Friction on Inclined Plane Calculator

Compute normal force, friction, downhill component, acceleration, and critical sliding angle with vector diagram

30°

Forces & Motion Analysis

Object accelerates down the slope
Critical Angle θ_crit = arctan(0.40) ≈ 21.8° (поточний кут 30° > 21.8°)
Acceleration (a)
1.51 м/с²
Net Downhill Force (F_net)
7.53 Н
Normal Force (N) N
42.48 Н
mg·cos(θ)
Downhill Force (Fg∥)
24.52 Н
mg·sin(θ)
Friction Force (F_f)
16.99 Н
μ·N (max 16.99Н)
Vector Free-Body Diagram
30°NF_fFg∥mg

How to use

  1. Enter object mass and inclination angle with horizontal.
  2. Specify kinetic friction coefficient μ (or 0 for frictionless slope).
  3. Obtain resultant net forces, along-plane acceleration, and motion dynamics.

Calculation Example

For a block on a frictionless 30° ramp with g = 9.81 m/s²:

Ramp angle: 30°

Friction coefficient: 0

Acceleration down the ramp: ≈ 4.91 m/s² (a = g * sin(30°))

With friction: a = g * (sin(α) - μ * cos(α)).

Calculation Methodology

Calculations employ Newton's second law of motion. Gravitational force decomposes into parallel driving force (m*g*sin(α)) and normal component supporting friction resistance (F_f = μ*m*g*cos(α)).

Frequently Asked Questions

What factors determine acceleration down an inclined plane?

Ramp angle, local gravity, and the surface kinetic friction coefficient.

How does friction affect downhill motion?

Friction opposes motion, reducing net acceleration. When tan(α) ≤ μ, the object remains stationary.

Does object mass affect downhill acceleration?

In basic friction and frictionless models, mass cancels out completely from the acceleration equation.

Can slide travel time and final velocity be determined?

Yes, using standard kinematic equations of uniformly accelerated motion given distance or time.

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