Forces, Friction & F = ma
Push a box across the floor or up a ramp. Weight, normal force and friction are added up along the surface, and Newton’s second law turns the net force into an acceleration — or tells you the box does not move at all.
Newton’s Three Laws
1. Without a net force, a thing keeps doing what it was doing: standing still or moving in a straight line at a steady speed. 2. A net force F gives a mass m an acceleration a = F/m. 3. Forces come in pairs: the floor pushes up on the box exactly as hard as the box pushes down on the floor.
Friction holds a box still up to a limit, μs·N. Push harder and the box breaks loose; while it slides, friction is usually a bit smaller, μk·N. That is why it is harder to get a heavy box moving than to keep it moving.
Forces, Step by Step
aKey Relations
Only the net force counts: all forces added up with their directions. Forces in newtons, mass in kilograms, acceleration in m/s².
Along the slope gravity pulls the box down; at right angles to it the surface pushes back with the normal force.
Static friction pushes back only as hard as needed, up to μsN. Once the box slides, kinetic friction is a fixed μkN against the motion.
Sources & Verification
- D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 5 (Force and Motion) and Ch. 6 (Friction).
- R. A. Serway & J. W. Jewett, Physics for Scientists and Engineers, 9th ed., Cengage, 2014 — Table 5.1, coefficients of friction (typical values; real surfaces vary).
Frequently Asked Questions
How do I calculate acceleration from force and mass?
Use Newton's second law, a = F/m, with the net force in newtons and the mass in kilograms. A 3000 N push on a 1200 kg car with no friction gives 3000 ÷ 1200 = 2.5 m/s². With friction, first subtract the friction force: only the net force accelerates the mass.
How do I calculate the friction force?
Friction = μ × N, the friction coefficient times the normal force. On a flat floor N equals the weight mg. A 10 kg box on a floor with μk = 0.4 has N = 98.1 N, so sliding friction is 0.4 × 98.1 = 39.24 N. Pushing it with 50 N leaves 10.76 N, an acceleration of 1.08 m/s².
What is the difference between static and kinetic friction?
Static friction holds something still and pushes back only as hard as needed, up to μs × N. Once it slides, kinetic friction takes over: a fixed μk × N against the motion, usually a bit smaller. That is why a heavy box is harder to get moving than to keep moving.
How do you calculate forces on an inclined plane?
Split the weight: along the slope gravity pulls with mg·sin θ, into the slope with mg·cos θ, which the normal force cancels. A 5 kg block on a 30° ramp feels 24.5 N down the slope and N = 42.5 N. With μs = 0.5 it slides, because tan 30° = 0.58 is more than 0.5; with μk = 0.4 it speeds up at 1.51 m/s².
What are Newton's three laws of motion?
1. Without a net force, an object stays at rest or keeps moving in a straight line at a steady speed. 2. A net force gives an acceleration a = F/m. 3. Forces come in pairs: if A pushes on B, B pushes back on A just as hard in the opposite direction.
What is the normal force?
The push of a surface at right angles to itself, which stops an object sinking into it. On a flat floor it equals the weight, mg; on a slope it is smaller, mg·cos θ, which is why friction is smaller on a slope too.