Dynamics: (c) weight of an object; W = mg

The idea

Weight is the gravitational force acting on an object, calculated as W = mg, where m is mass in kilograms and g is gravitational field strength in newtons per kilogram (N kg⁻¹). On Earth, g ≈ 9.81 N kg⁻¹, so a 2.0 kg mass has weight W = 2.0 × 9.81 = 19.62 N. Weight is a vector directed towards the centre of the gravitating body. Mass is a scalar measure of inertia, constant everywhere, while weight varies with g. Always convert grams to kilograms before substituting. The equation applies to a uniform gravitational field, which is a good approximation near a planet's surface.

What earns the marks

• Weight is the gravitational force on an object, given by W = mg.
• m is mass in kg; g is gravitational field strength in N kg⁻¹.
• Weight is a vector directed towards the centre of the gravitating body.
• Mass is a scalar and constant; weight varies with gravitational field strength.
• Typical value on Earth: g ≈ 9.81 N kg⁻¹, so W = mg gives weight in newtons.
• Correct unit conversion: 1 g = 1 × 10⁻³ kg before substitution.

Common mistakes and how to put them right

• Confusing mass and weight.

  Put it right by stating W = mg and using newtons for weight.

• Using grams directly in W = mg.

  Put it right by converting mass to kilograms first.

• Treating g as 10 N kg⁻¹ when the question expects 9.81 N kg⁻¹.

  Put it right by using the value given or the standard 9.81 N kg⁻¹ unless told otherwise.

• Thinking weight is always the same everywhere.

  Put it right by recognising g varies.

Exam tips

• Underline the mass value and its unit in the question; convert to kg immediately if it is in grams.
• Write the equation W = mg, substitute numbers with units, and give the answer in newtons.
• Check whether the question asks for weight or mass; the unit N indicates weight, kg indicates mass.