Mass and weight

The weight of an object is the force acting on the object's mass due to gravity. The weight of an object can be practically measured using a newtonmeter, which is a spring balance.

The weight of an object and its mass are directly proportional. This means that, for a given gravitational field strength, doubling the mass would double the weight.

Scientists write this type of relationship in a short form as:

\text{W} \alpha \text{m}

Weight can be calculated using the equation:

weight = mass × gravitational field strength

\text{W} = \text{mg}

This is when:

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

The Moon is smaller and has less mass than the Earth, so its gravitational field strength is only about one-sixth of the Earth's. For example, a 120 kg astronaut weighs 1,200 N on Earth but only 200 N on the Moon. Remember that the mass would still be 120 kg.

On Earth, an astronaut has a mass of 120 kg. His weight is 120 x 10 = 1200 N. On the moon his mass is still 120 kg but his weight is only 200 N.

Example

An apple has a mass of 100 g. Calculate its weight on Earth ( \text{g} = 9.8 N/kg).

100 g = 100 ÷ 1000 = 0.1 kg

\text{W} = \text{mg}

\text{W} = 0.1 kg × 9.8 N/kg

\text{W} = 0.98 N

Question

Calculate the weight of a 30 kg dog ( \text{g} = 9.8 N/kg).

\text{W} = \text{mg}

\text{W} = 30 kg × 9.8 N/kg

\text{W} = 294 N