Forces, mass and weight

A force is a push or a pull on an object, caused by it interacting with something else.

Forces are measured in newtons (N).

Every force has a size and a direction, so force is a vector. A quantity with a size only is a scalar.

• Vectors: force, weight, velocity, displacement, acceleration, momentum.
• Scalars: mass, speed, distance, time, energy, temperature.

On a diagram a vector is an arrow: its length shows the size, and it points in the direction of the force.

Contact forces need the objects to touch: friction, air resistance (drag), tension, the normal contact force from a surface, and upthrust in a fluid.

Non-contact forces act across a gap: gravitational force (weight), magnetic force and electrostatic force.

Forces come in pairs between two objects. The Earth pulls you down; you pull the Earth up with a force just as big.

Weight is the force of gravity on a mass.

Near the Earth it depends on the gravitational field strength, g.

weight = mass × gravitational field strength
W = m g

Weight in N, mass in kg, g in N/kg. All three boards: recall this one. On Earth g = 9.8 N/kg; the question will say which value to use.

1. A 250 g bag of rice: mass = 250 ÷ 1000 = 0.25 kg
2. W = 0.25 × 9.8
3. W = 2.45 N

Mass is the amount of matter and is the same everywhere. Weight changes with g: on the Moon (g = 1.6 N/kg) you weigh about a sixth as much, but your mass is the same.

Weight and mass are directly proportional: double the mass, double the weight. Weight is measured with a calibrated spring balance (a newtonmeter).

The weight of an object acts as if it all pulls at one point, its centre of mass.

For a uniform, symmetrical object it is in the middle: the 50 cm mark on a metre rule, or where the diagonals of a rectangle cross. On a diagram, draw the weight arrow down from the centre of mass.