The difference between mass and weight, weight as W = m g, the meaning of gravitational field strength, and how an object reaches terminal velocity as air resistance balances weight.

What this dot point is asking

CCEA Double Award wants you to tell mass from weight, use W = m g, explain gravitational field strength, and describe how a falling object reaches terminal velocity in terms of the forces acting. The terminal-velocity explanation is a common extended-response question.

Mass and weight

So a person has the same mass on the Earth and the Moon, but a smaller weight on the Moon because the Moon's gravity is weaker.

Weight, mass and gravitational field strength

Gravitational field strength is the force of gravity on each kilogram of mass. It is larger on planets with more mass and smaller on the Moon.

Terminal velocity

When an object falls through air, two forces act: its weight (downward) and air resistance (upward, increasing with speed).

Gravitational field strength across the Solar System

Because weight depends on the gravitational field strength, the same object has different weights on different bodies. On the Moon $g$ is about $1.6\ \text{N/kg}$, roughly a sixth of Earth's, so a $60\ \text{N}$ object on Earth weighs only about $10\ \text{N}$ on the Moon. On Jupiter, with much more mass, $g$ is larger and the same object would weigh more. In every case the mass stays the same, because mass is the amount of matter, and only the weight (a force) changes.

Examples in context

Example 1. Weighing scales

A bathroom scale really measures weight (a force) but displays mass by dividing by $g$. On the Moon the same scale would read a smaller value, even though your mass is unchanged.

Example 2. A feather and a hammer

On the Moon, with no air resistance, a feather and a hammer fall together and land at the same time, because both accelerate at the same $g$. On Earth the feather falls more slowly only because air resistance acts more on it relative to its small weight.

Example 3. A parachutist before and after opening the parachute

Before opening, the parachutist reaches a high terminal velocity where air resistance equals weight. Opening the parachute suddenly increases the air resistance so it exceeds the weight; the resultant force is now upward, so the parachutist slows down until air resistance again equals weight, giving a new, much lower terminal velocity safe for landing.

Try this

Q1. State the difference between mass and weight. [2 marks]

• Cue. Mass is the amount of matter (kg) and is constant; weight is the force of gravity (N) and depends on location.

Q2. Calculate the weight of a $50\ \text{kg}$ student on Earth ($g = 10\ \text{N/kg}$). [2 marks]

• Cue. $W = m g = 50 \times 10 = 500\ \text{N}$.

Q3. What is happening to the forces on an object falling at terminal velocity? [1 mark]

• Cue. Air resistance equals weight, so the resultant force is zero.