2.16 - Mass, Weight & Gravity

Gravity is the force of attraction between masses

• Everything with mass has a gravitational field around it, which attracts other masses.
• Gravity is always attractive, and the more massive an object is, the stronger its gravitational field.
• Gravity acts between any two masses, but the pull is only noticeable when at least one mass is very large, such as a planet or star.

Near the surface of a planet, gravity:

• Makes objects fall towards the ground.
• Gives every object a weight.

Weight and mass are not the same

• Mass - The amount of matter in an object. Measured in kilograms (kg). Mass doesn't depend on location, so an object has the same mass anywhere in the universe. It's a scalar quantity.
• Weight - The force acting on an object due to gravity. Weight is a force, so it's measured in newtons (N) using a calibrated spring balance (a newtonmeter).
• Weight acts as though it's concentrated at a single point on the object, called the centre of mass.

Why weight changes with location

• Weight depends on the gravitational field strength where the object is.
• An object has different weights in different places, even though its mass never changes.
• A 1 kg mass weighs about 10 N on Earth but only about 1.6 N on the Moon, because the Moon's gravitational field strength is smaller.

Formula for weight

Where:

• $W$ = Weight, in newtons (N)
• $m$ = Mass, in kilograms (kg)
• $g$ = Gravitational field strength, in newtons per kilogram (N/kg)

Values of g

• On Earth, $g$ is about 10 N/kg - always use the value given in the question.
• On the Moon, $g$ is about 1.6 N/kg, and it's different again on other planets.
• Weight and mass are directly proportional ($W\propto m$) for a given gravitational field strength.

Worked example - Weight of a suitcase

A 6.0 kg suitcase is on Earth, where the gravitational field strength is 10 N/kg. Calculate its weight.

g is also the acceleration of free fall

• Gravitational field strength, $g$, is also the acceleration of an object in free fall.
• Free fall is the motion of an object when the only force acting on it is gravity.
• Near the Earth's surface, a falling object accelerates at about 9.8 m/s² (often rounded to 10 m/s²), so $g$ can be written in units of N/kg or m/s².

All objects fall at the same rate

• With no air resistance, every object near the Earth's surface falls with the same acceleration, regardless of its mass.
• Gravity pulls harder on a heavier object, but a heavier object also has more mass to accelerate - the two effects cancel out.
• Without air resistance, a falling object's speed increases by about 9.8 m/s every second.