Recall and apply: gravitational force (N) = mass (kg) × gravitational…

The idea

Weight is the gravitational force on a mass, and the equation W = m × g links them. Mass in kilograms measures how much matter is present; gravitational field strength g in newtons per kilogram tells you the force on each kilogram. On Earth g is about 9.8 N/kg, so a 5 kg bag has a weight of 5 × 9.8 = 49 N. On the Moon g is about 1.6 N/kg, so the same 5 kg bag weighs 5 × 1.6 = 8 N while its mass stays 5 kg. To apply the equation, identify m and g, multiply, and attach the unit N. To rearrange, divide weight by g to find mass, or divide weight by mass to find g. Check that the unit N/kg is equivalent to m/s², since a newton per kilogram is the same as a metre per second squared.

What earns the marks

• Multiplies mass in kilograms by gravitational field strength in newtons per kilogram to obtain weight in newtons.
• States that mass stays constant while weight changes when gravitational field strength changes.
• Rearranges the equation to find mass by dividing weight by gravitational field strength.
• Uses g ≈ 9.8 N/kg for Earth and recognises a smaller g gives a smaller weight for the same mass.
• Attaches the unit newton to a calculated force and the unit kilogram to a mass.

Common mistakes and how to put them right

• Confuses mass with weight.

  Put it right: Keep mass in kilograms and weight in newtons.

• Uses the value of g for the wrong location.

  Put it right: Match g to the planet or Moon named in the question.

• Forgets to convert grams to kilograms.

  Put it right: Divide grams by 1000 before multiplying.

• Omits the unit on the answer.

  Put it right: Write N after a force value.

Exam tips

• Write the equation, substitute the numbers with units, then give the answer with its unit.
• Check whether the question asks for mass or weight before rearranging.
• Use the value of g stated in the question rather than assuming Earth's value.