Forces and Motion

Newton's Three Laws of Motion

First Law: An object remains at rest or moves at constant velocity unless acted upon by a resultant force.

Implication: if an object is stationary or moving at constant speed, all forces are balanced (resultant = 0).

Second Law: The resultant force on an object is directly proportional to the acceleration it produces and inversely proportional to the object's mass.

F = ma (resultant force in N, mass in kg, acceleration in m/s²)

Third Law: When object A exerts a force on object B, object B exerts an equal and opposite force on object A.

These forces act on different objects — they are NOT balanced forces. Example: Earth pulls you down (gravity), you pull Earth up (equal magnitude, opposite direction).

Mass and Weight

• Mass (kg): the amount of matter in an object. It does not change with location.
• Weight (N): the gravitational force on an object. W = mg.
• On Earth: g ≈ 9.8 N/kg (use 10 N/kg unless told otherwise in Edexcel).
• On the Moon (g ≈ 1.6 N/kg): a 70 kg person weighs 70 × 1.6 = 112 N.

Resultant Forces and Free Body Diagrams

When multiple forces act on an object, find the resultant (net) force:

• Collinear forces (same line): add/subtract.
• Perpendicular forces: use Pythagoras.

Free body diagrams show all forces acting on a single object as arrows from a centre dot, labelled with size and direction.

Terminal Velocity

A falling object experiences:

1. Weight (downward) — constant.
2. Air resistance / drag (upward) — increases with speed.

Initially weight > drag → accelerates. As speed increases, drag increases → resultant force decreases → acceleration decreases. When drag = weight → terminal velocity (constant speed, zero acceleration).

Parachutist example: opens parachute → drag suddenly increases greatly → resultant force upward → decelerates → new (lower) terminal velocity reached.

Momentum

Momentum (p) = mass × velocity (unit: kg m/s).

Conservation of momentum: in a closed system (no external forces), total momentum before = total momentum after.

For a collision: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Impulse = force × time = change in momentum (Ft = mv − mu)

Airbags and crumple zones increase collision time → reduce force for same momentum change → safer.

Core Practical 2 — Investigating Force, Mass and Acceleration

Equipment: dynamics trolley, ramp (compensated for friction), hanging masses on string over pulley, light gates + data logger (or ticker tape).

Method:

1. Keep total system mass constant. Vary the hanging mass (force) and measure acceleration.
2. Then keep force constant; add masses to the trolley and measure acceleration.

Results:

• a ∝ F (at constant mass): graph of a vs F is a straight line through origin.
• a ∝ 1/m (at constant force): graph of a vs 1/m is a straight line through origin.

Key detail: the mass of the hanging mass string must be small compared to total system mass, otherwise you can't treat the hanging mass as a force alone.