Gravity: W = m g

The idea

This equation links the weight of an object to its mass and the gravitational field strength at its location. Weight is the force of gravity acting on a mass, measured in newtons (N). Mass is the amount of matter, measured in kilograms (kg), and does not change with location. Gravitational field strength, g, is the force per kilogram, measured in newtons per kilogram (N/kg). On Earth g is about 9.8 N/kg, often rounded to 10 N/kg for estimates. To use the equation, identify the mass in kg and the value of g for the planet or moon, then multiply: for example, a 2 kg bag has weight W = 2 kg × 9.8 N/kg = 19.6 N on Earth, but only about 3.2 N on the Moon where g is about 1.6 N/kg. Rearranging gives m = W ÷ g or g = W ÷ m, so the same equation lets you find mass from weight or compare field strengths.

What earns the marks

• State that W is weight in newtons (N), m is mass in kilograms (kg) and g is gravitational field strength in newtons per kilogram (N/kg).
• Substitute values correctly into W = m g, keeping units consistent, for example W = 2 kg × 9.8 N/kg = 19.6 N.
• Recognise that g varies with location, so the same mass has different weights on Earth, the Moon or Mars.
• Rearrange the equation to find mass or gravitational field strength when the other two quantities are known.
• Explain that mass is a scalar amount of matter in kg while weight is a force in N, so they are not the same quantity.

Common mistakes and how to put them right

• Using mass in grams without converting to kilograms.

  Put it right by dividing grams by 1000 before multiplying by g.

• Writing the unit of weight as kg or N/kg.

  Put it right by giving weight in newtons (N) because it is a force.

• Assuming g is always 9.8 N/kg everywhere.

  Put it right by using the value for the relevant location, such as about 1.6 N/kg on the Moon.

Exam tips

• Write the equation, then substitute numbers with units before calculating so the examiner can see your method.
• Check whether the question gives mass or weight; if it gives weight and asks for mass, rearrange to m = W ÷ g.
• Round g to 10 N/kg only when the question says to estimate, otherwise use 9.8 N/kg for Earth.
• Give the unit N with every weight answer and kg with every mass answer.