Newton's second law — the formula F = ma: force, mass, acceleration
What we'll do: We'll apply a force to a block of varying mass and watch how its acceleration changes.
What you see on screen: A block with a force arrow, sliders for force and mass (and optionally friction) and an acceleration vector. A heavier block speeds up more slowly; the relation bar shows a = F/m. Readouts: force, mass, acceleration and the current velocity.
What just happened?
Same force, but a heavier block — and the acceleration dropped by half. Force and mass act on acceleration in opposite ways.
Newton’s second law:
Acceleration is directly proportional to the net force and inversely proportional to the mass.
What does it mean?
Push harder → you speed it up faster (a grows with F). Heavier body → harder to speed up (a drops with m). The same force gives a light body a large acceleration and a heavy one a small one.
Watch the net force:
the NET force is what counts. If friction acts, acceleration comes only from the excess of the driving force over resistance:
Why you need it for the exam:
F = ma is the most used formula in dynamics. The trick: find the net force, divide by the mass — you have the acceleration; then kinematics (v = at, s = ½at²).
Remember: acceleration grows with force and drops with mass — a = F/m. The quantitative heart of mechanics.
Theory & formulas
Newton's second law
The acceleration of a body is directly proportional to the net force and inversely proportional to the mass:
What it means
- the same force on a larger mass gives a smaller acceleration,
- a larger force on the same mass gives a larger acceleration.
Net force
Acceleration is determined by the net (resultant) force — the sum of all forces, accounting for e.g. friction. When the forces balance (), the acceleration is zero.
Notation: — net force, — mass of the body, — acceleration.
Frequently asked questions
›How is Newton's second law of motion stated?
The acceleration of a body is directly proportional to the net force and inversely proportional to the mass: F = ma.
›What happens to the acceleration when the mass increases?
It decreases — for the same force, acceleration is inversely proportional to the mass.
›Which force determines the acceleration?
The net (resultant) force — the sum of all forces, accounting for e.g. friction.
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