Mass, weight, density and forces
Mass and weight, density, the effects of forces, springs, resultant force, moments and momentum.
📌 Key points
- Mass is the quantity of matter in an object (kg). Weight is the gravitational force on it (N): W = mg, with g = 9.8 N/kg on Earth.
- Gravitational field strength g is the force per unit mass. Mass is the same everywhere; weight changes with g (e.g. less on the Moon).
- Density ρ = mV. Find the volume of an irregular solid by displacement in a measuring cylinder. An object floats in a liquid if it is less dense than the liquid.
- Forces can change an object’s speed, direction or shape. Up to the limit of proportionality, extension is proportional to load; spring constant k = Fx.
- If the resultant force is zero, an object stays at rest or moves at constant velocity. Otherwise it accelerates: F = ma.
- Friction and air resistance act against motion and transfer energy to thermal stores. An object moving in a circle at constant speed needs a force towards the centre.
- Moment = force × perpendicular distance from the pivot. In equilibrium the clockwise moments equal the anticlockwise moments and there is no resultant force.
- An object is more stable if its centre of gravity is low and its base is wide.
- Momentum p = mv (kg m/s). Impulse = FΔt = Δ(mv). In collisions and explosions, total momentum is conserved.
📖 Key terms
- Mass
- The quantity of matter in an object; measured in kg.
- Weight
- The gravitational force on an object that has mass; measured in N.
- Gravitational field strength
- Force per unit mass (N/kg).
- Density
- Mass per unit volume.
- Limit of proportionality
- The point beyond which extension is no longer proportional to load.
- Moment
- Force × perpendicular distance from the pivot.
- Centre of gravity
- The point through which the whole weight of an object appears to act.
- Momentum
- Mass × velocity.
✏️ Worked example
A 0.40 kg ball moving at 5.0 m/s hits a wall and bounces straight back at 3.0 m/s. The contact time is 0.10 s. Find the impulse and the average force on the ball.
- Take the original direction as positive. Initial momentum = 0.40 × 5.0 = +2.0 kg m/s.
- Final momentum = 0.40 × (−3.0) = −1.2 kg m/s.
- Impulse = change in momentum = −1.2 − 2.0 = −3.2 N s (size 3.2 N s).
- Average force = impulsetime = 3.20.10 = 32 N, away from the wall.
Weight is a force, so it is measured in newtons — never write a weight in kilograms. When an object bounces back, its velocity changes sign.
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