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Friction & Inclined Plane Lab

Investigate how friction prevents motion on inclined surfaces. Vary the angle, mass, and surface material to discover the critical angle where a block transitions from static to kinetic friction and begins to slide.

Guided Experiment: Finding the Critical Angle

If you slowly increase the incline angle, at what angle do you predict the block will start sliding? How does this relate to the coefficient of static friction?

Write your hypothesis in the Lab Report panel, then click Next.

Controls

Mass2.0 kg
Angle20 deg
Static Friction (μs)0.50
Kinetic Friction (μk)0.30
Gravity9.81 m/s²

Force Analysis

STATIC — friction holds the block
fs≤μsNθ<θc=26.6°f_s \le \mu_s N \quad \theta < \theta_c = 26.6°
Normal Force N
18.437 N
Parallel Force F‖
6.710 N
Max Static Friction
9.218 N
Kinetic Friction
5.531 N
Applied Friction
6.710 N
Net Force
0.000 N
Weight
19.62 N
Critical Angle
26.57°
Coefficients: μs = 0.50, μk = 0.30
θ = 20° < θc = 26.6°

Forces vs Angle

Normal Force (N) Parallel Force (F‖) Max Static Friction Kinetic Friction Critical Angle

Data Table

(0 rows)
#TrialAngle(deg)Normal Force(N)F parallel(N)Friction(N)Sliding?Acceleration(m/s²)
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0 / 500
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Reference Guide

Friction Forces

Two types of friction act between surfaces in contact.

fs≤μsNfk=μkNf_s \le \mu_s N \qquad f_k = \mu_k N

Static friction adjusts to prevent motion up to its maximum. Kinetic friction is constant once sliding begins. Always μk≤μs\mu_k \le \mu_s.

Static vs Kinetic

Before sliding, static friction exactly balances the gravitational component along the slope:

fs=mgsin⁡θ(θ<θc)f_s = mg\sin\theta \quad (\theta < \theta_c)

Once sliding, kinetic friction is fixed and the block accelerates:

a=g(sin⁡θ−μkcos⁡θ)a = g(\sin\theta - \mu_k \cos\theta)

The Critical Angle

The block starts sliding when the parallel force exceeds maximum static friction. Setting them equal:

θc=arctan⁡(μs)\theta_c = \arctan(\mu_s)

This is independent of mass. A heavier block has proportionally larger friction and parallel force, so they cancel out.

Inclined Plane Analysis

Resolving gravity along and perpendicular to the surface:

N=mgcos⁡θF∥=mgsin⁡θN = mg\cos\theta \qquad F_\parallel = mg\sin\theta

The normal force decreases and the parallel component increases as the angle rises. Their ratio gives tan⁡θ\tan\theta, which equals μs\mu_s at the critical angle.