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Forces & Motion

How to use this simulation

A block sits on a horizontal surface. Choose its mass and the forward force, then predict whether it stays still or speeds up. GCSE mode reveals the friction coefficient μ. The model uses one value of μ and ignores air resistance, so the only horizontal forces are the applied force and friction.

  1. Start from the default mass and a small applied force. Before you move the slider, decide whether the resultant force is zero.
  2. Increase the applied force. The block does not move until that force is greater than the friction limit, μmg.
  3. Once it is accelerating, keep the resultant force the same and increase the mass. Acceleration falls, because a = F/m.
  4. Drop the applied force back below μmg. Friction then matches the applied force, the resultant force is zero, and the block — released from rest in this model — stays still.

Key ideas

Newton’s first law

If the forces on the block are balanced, it does not start moving. Weight mg acts downward and the normal contact force acts upward with the same size, so those two forces cancel and do not affect the horizontal motion.

Newton’s second law

The resultant force equals mass × acceleration: F = ma. Acceleration is in the same direction as the resultant force. Doubling the resultant force doubles the acceleration; doubling the mass halves it. This is the relationship the live readouts use.

Limiting friction

Friction opposes the applied force and increases to match it, up to a maximum of μmg, with g = 9.81 m/s². Below that limit the resultant force is zero. Above it, resultant force = applied force − μmg and the block accelerates.

A worked check

A 10 kg block with μ = 0.2 has a friction limit of 0.2 × 10 × 9.81 = 19.6 N. An applied force of 20 N leaves only about 0.4 N resultant, so the acceleration is very small. An applied force of 80 N leaves about 60 N resultant and a much larger acceleration.

Where this sits in the course

Upper primary and GCSE use the idea of balanced and unbalanced forces and F = ma. A level and IB add the model F ≤ μR for friction on a rough surface. The simulation is the horizontal case of that model.

What the model leaves out

Motion is in a straight line. μ does not change with speed, and there is no air resistance. A real object needs a continued driving force to travel at a steady speed whenever friction or drag is still acting.