Definition
- Weight is the pull that a gravitational field exerts on any object that has mass
- Because weight is a force, it carries a direction (always towards the centre of the planet), making weight a vector quantity; weight is measured in newtons (N)
- Mass is the amount of matter in an object, a scalar quantity measured in kilograms (kg)
- Mass and weight are not the same physical quantity even though everyday language often confuses them
The equation
W = m × g
- where:
- W = weight (N)
- m = mass (kg)
- g = gravitational field strength (N/kg)
- g on Earth is 10 N/kg (also equal to the acceleration of free fall, 10 m/s², because these two numerical values match when they describe the same physical effect from two different angles)
- g varies between planets and moons: a stronger gravitational field gives a larger weight for the same mass
- Mass and weight are directly proportional to one another in a given gravitational field, so doubling the mass doubles the weight
Example — a Mars rover has a mass of 800 kg. Earth's gravitational field strength is 10 N/kg and Mars's is 3.7 N/kg. Calculate the rover's weight on each planet.
- Weight on Earth = m × g = 800 × 10 = 8000 N
- Weight on Mars = m × g = 800 × 3.7 = 2960 N
- Same rover, same mass, but its weight on Mars is much smaller because the Martian gravitational field is weaker