Weight, mass and gravitational field strength (Gravity)

All objects with mass produce a gravitational field around them. The more mass an object has, the greater its gravitational field will be.

Planet size and gravitational field strength

Gravitational field strength (g) is measured in newtons per kilogram (N/kg). The Earth's gravitational field strength at, or close to, the surface is 10 N/kg. This means that for each kilogram of mass, an object will experience 10 N of force.

Where there is a weaker gravitational field, the weight of an object is smaller. For example, the gravitational field strength of the Moon is 1.6 N/kg. This means that for each kilogram of mass, an object will experience 1.6 N of force. Therefore, an astronaut will weigh less on the Moon than they do on the Earth.

Weight is the force acting on an object due to gravity - it has the unit newtons (N) and acts towards the centre of a gravitational field. The weight of an object can be measured using a spring-balance often called a force meter calibrated in newtons and sometimes called a newton meter.

Weight is a non-contact force because gravity exerts its force through a field. An object does not need to be touching the Earth to have a weight.

Objects on the Moon weigh less than they do on the Earth because the gravitational field strength is much less. On the Moon, astronauts can jump higher and leap farther than on Earth. Gravitational field strength is in direct relation to the size of a planet.

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.

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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 ÷ 1,000 = 0.1 kg

W = m g

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

W = 1.00~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