Gravity: weight = mass × gravitational field strength

The idea

This equation links three quantities: weight (W) in newtons, mass (m) in kilograms and gravitational field strength (g) in newtons per kilogram. Weight is the force of gravity on an object, so it depends on where the object is. Mass is the amount of matter and does not change with location. For example, a 60 kg student has weight 60 × 9.8 = 588 N on Earth, but on the Moon g is about 1.6 N/kg, so the same student weighs 60 × 1.6 = 96 N. The equation can be rearranged: m = W ÷ g and g = W ÷ m. When using it, keep units consistent and remember that g is a property of the place, not of the object.

What earns the marks

• Identify W as weight in newtons, m as mass in kilograms and g as gravitational field strength in N/kg.
• Substitute values into weight = mass × gravitational field strength and calculate correctly.
• Rearrange the equation to find mass (m = W ÷ g) or gravitational field strength (g = W ÷ m).
• Explain that g varies between planets and moons, so weight changes but mass does not.
• Use the equation to compare weights of the same mass on Earth and on another body.

Common mistakes and how to put them right

• Mixing up mass and weight.

  Put it right: Mass is in kg and does not change with location; weight is in N and changes with g.

• Forgetting to convert grams to kilograms before multiplying.

  Put it right: 500 g must be written as 0.5 kg.

• Using the wrong rearrangement.

  Put it right: Find mass, divide weight by g, not multiply.

Exam tips

• Show the equation, the substitution and the answer with its unit to gain method and accuracy credit.
• Convert units before calculating, for example grams to kilograms.
• Use the value of g given in the question; if none is given, use 9.8 N/kg.