Mass and weight
The The force acting on an object due to the pull of gravity from a massive object like a planet. The force acts towards the centre of the planet and is measured in newtons (N). 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 Relationship between two variables where one variable is equal to a constant multiplying the other variable. Variables are plotted as a straight line though the origin.. This means that, for a given Force per unit mass. Measured in newtons per kilogram (N/kg)., 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.
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