What is Newton's second law?

The resultant force on an object equals its mass times its acceleration, F = ma. Double the resultant force and the acceleration doubles; double the mass and it halves.

Why doesn't the block move when I push gently?

Friction matches your push up to a limit of μs times the weight. Only when the applied force beats that limit does a resultant force appear and the block starts to accelerate.

Why is the velocity-time graph a straight line?

With a constant resultant force the acceleration is constant, and acceleration is the gradient of a velocity-time graph.

How much force do I need for a given acceleration with friction?

Add the force for the acceleration to the friction: F = m(a + μg). A 5 kg block with μ = 0.2 needs F = 5 × (2 + 0.2 × 9.8) = 19.8 N to accelerate at 2 m/s². That is more than the 9.8 N of static grip, so it does get going. Pick Force needed under Solve for to see each step.

← All simulations

Forces & acceleration

Push a block across a rough surface: net force, not applied force, sets the acceleration.

Just need the number? Physics Formulas

Velocity vs time

Readouts

What's happening

Friction opposes motion with force μmg. While the applied force is smaller than that, the block stays put or slows down. Above it, the net force F − μmg accelerates the mass, and the velocity-time graph becomes a straight line whose slope is exactly a = F_net/m.

a = (F − μmg) / m

GCSE Physics (AQA 4.5.6, Edexcel, OCR): resultant forces, Newton's second law and friction. A-Level Maths mechanics: F = ma with friction.

Work through the numbers with SUVAT Solver.

Challenge

Predict first: with m = 5 kg and μ = 0.4, what applied force is needed before the block moves at all? Compute μmg, then test it.

FAQ

What is Newton's second law?: The resultant force on an object equals its mass times its acceleration, F = ma. Double the resultant force and the acceleration doubles; double the mass and it halves.
Why doesn't the block move when I push gently?: Friction matches your push up to a limit of μs times the weight. Only when the applied force beats that limit does a resultant force appear and the block starts to accelerate.
Why is the velocity-time graph a straight line?: With a constant resultant force the acceleration is constant, and acceleration is the gradient of a velocity-time graph.
How much force do I need for a given acceleration with friction?: Add the force for the acceleration to the friction: F = m(a + μg). A 5 kg block with μ = 0.2 needs F = 5 × (2 + 0.2 × 9.8) = 19.8 N to accelerate at 2 m/s². That is more than the 9.8 N of static grip, so it does get going. Pick Force needed under Solve for to see each step.