Weight, mass and gravitational field strength

The weight of an object may be thought of as acting at a single point called its centre of mass. Depending on the object's shape, its centre of mass can be inside or outside it.

The weight of an object and its mass are directly proportional. For a given gravitational field strength, the greater the mass of the object - the greater its weight is.

Weight can be calculated using the equation:

weight = mass × gravitational field strength

  W = m \ g

This is when:

  • weight (W) is measured in newtons (N)
  • mass (m) is measured in kilograms (kg)
  • gravitational field strength (g) is measured in newtons per kilogram (N/kg)

Example

An apple has a mass of 100 g. Calculate its weight on Earth (g = 10 N/kg).

100 g = 100 ÷ 1000 = 0.1 kg

  W = m \ g

  W = 0.1 \ kg \times 10 \ N/kg

  W = 1.0 \ N

Question

Calculate the weight of a 30 kg dog (g = 10 N/kg).

  W = m \ g

  W = 30 \ kg \times 10 \ N/kg

  W = 300 \ N

Measuring weight

To make a measurement of weight, we have to measure the force pulling the object towards the centre of the Earth. We do this by balancing it with a known force. If the object is stationary, Newton's third law then tells us that the known force is the same as the weight.

A spring balance scale has a pile of marbles on its scale, which weigh it down. This shows the force from the spring and the marble's weight.

A spring balance will stretch until the force from the spring is enough to balance the weight of the object, and the distance the spring in it has stretched indicates the force it is exerting to hold up the object.

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