Force and friction, explained.
Static friction adjusts to oppose a push, up to μsN. If the push exceeds that limit, the block begins to slide. Kinetic friction then acts against sliding motion. On this level surface with no vertical acceleration, N = mg.
The relationship to remember
Key formulas
- Normal force on a level surface
- N = mg
- No vertical acceleration
- Static friction
- fₛ ≤ μₛN
- Matches the push up to this limit
- Kinetic friction
- fₖ = μₖN
- Opposes the sliding motion
- Friction on level ground
- f = μmg
- Shortcut when N = mg
- Newton’s second law
- Fnet = ma
- Once sliding, a = (F − fₖ)/m
Worked example
Problem. A 5 kg box rests on a level floor with μₛ = μₖ = 0.3. Someone pushes it horizontally with 20 N. Does it slide, and if so, what is its acceleration?
- Normal force: N = mg = 5 × 9.81 = 49.05 N.
- Maximum static friction: μN = 0.3 × 49.05 = 14.715 N. The 20 N push is larger, so the box starts to slide.
- Kinetic friction is μN = 14.715 N, so the net force is 20 − 14.715 = 5.285 N.
- Acceleration: a = Fnet/m = 5.285 / 5 = 1.057 m/s².
Answer. The box slides and accelerates at about 1.06 m/s².
A quick check
For a 5 kg block with μ = 0.3, the static-friction limit is 14.715 N. A 20 N push produces 5.285 N net force and acceleration 1.057 m/s².
Inside the default experiment
- Normal force N = mg = 5 × 9.81 = 49.05 N.
- Maximum static friction = μN = 14.71 N. Actual opposing friction = 14.71 N.
- Net force = 20 − 14.71 = 5.29 N. Acceleration = Fnet/m = 1.06 m/s².
When this model applies
Horizontal surface, rightward applied force, g = 9.81 m/s². For comparison, static and kinetic coefficients both equal μ. The block starts at rest.
Make a prediction. Then test it.
Find the smallest push that overcomes static friction.
Try it: Force & friction simulator ↗Frequently asked questions
Wondering about the why? Start here.
Why is the block not moving with a small force?
Static friction balances the applied force while the force is at or below its maximum. The net horizontal force is then zero.
Why do the force arrows use the same scale?
A shared arrow scale lets you compare opposing forces. Equal arrows mean zero net force; their difference determines acceleration.