The weight of an object and the mass of an object are directly proportional.

The idea

Weight and mass are directly proportional, which means their ratio is constant for a given gravitational field. The equation is W = m × g, where W is weight in newtons (N), m is mass in kilograms (kg) and g is gravitational field strength in newtons per kilogram (N/kg). On Earth, g is about 9.8 N/kg, so a 2 kg mass has a weight of about 19.6 N. If mass doubles, weight doubles; if mass triples, weight triples. A graph of weight on the y-axis against mass on the x-axis is a straight line through the origin, and its gradient equals g. On the Moon, g is smaller, so the same mass has less weight, but the mass does not change. Direct proportionality is therefore a mathematical relationship, not a statement that weight and mass are the same quantity.

What earns the marks

• Weight is the force of gravity on an object, measured in newtons (N); mass is the amount of matter, measured in kilograms (kg).
• The relationship is W = m × g, where g is the gravitational field strength in N/kg.
• Direct proportionality means W/m is constant, so doubling the mass doubles the weight.
• A graph of weight against mass is a straight line through the origin, and the gradient is equal to g.
• The value of g varies with location, so the same mass has different weights on different planets or moons.
• Mass is unchanged by location, but weight changes when gravitational field strength changes.

Common mistakes and how to put them right

• Writing W = m/g or W = g/m.

  Put it right by remembering that weight is the product of mass and gravitational field strength, W = m × g.

• Treating weight and mass as the same quantity.

  Put it right by stating that mass is in kg and is a scalar amount of matter, while weight is a force in N and depends on g.

• Using g = 10 N/kg and then giving an answer in kg.

  Put it right by checking that the unit of the result matches the quantity calculated: weight must be in N.

Exam tips

• Show the equation W = m × g, substitute the values with units, and give the unit N in your final answer.
• When describing a graph, state that it is a straight line through the origin and that the gradient equals gravitational field strength.
• If a question compares two locations, calculate weight at each location using the appropriate g value and state that mass stays the same.