Mass

Mass is a measure of the quantity of matter in an object at rest relative to the observer. It is measured in kilograms, written as $\mathrm{kg}$ .

Mass is different from weight, which is the gravitational force acting on an object. Moving an object to a different gravitational field can change its weight, but it does not change its mass simply because it has been moved.

Comparing masses with a balance

A two-pan balance compares the weights of objects placed in its pans. When the pans balance, the objects have equal weights. If both objects are in the same gravitational field, equal weights indicate equal masses. The balance can therefore compare their masses.

Weight

Weight is the gravitational force acting on an object because it has mass. It acts towards the body exerting the gravitational attraction. For example, an object near Earth has weight directed towards Earth.

Like other forces, weight is measured in newtons ( $\mathrm{N}$ ).

Weight, mass and gravitational field strength

An object’s weight depends on both its mass and the gravitational field strength at its location:

W = mg

Here, $$$W$$$ is weight in newtons ( $\mathrm{N}$ ), $$$m$$$ is mass in kilograms ( $\mathrm{kg}$ ), and $$$g$$$ is gravitational field strength in newtons per kilogram ( $\mathrm{N/kg}$ ). Gravitational field strength tells us the gravitational force on each kilogram of mass at that location.

For the same gravitational field strength, an object with more mass has more weight. If the object moves to a location with a different gravitational field strength, its weight changes even though its mass stays the same.

Gravitational field strength

A gravitational field exerts a force on an object with mass. At a particular location, gravitational field strength tells us how much gravitational force acts on each kilogram of mass.

The gravitational force on an object is its weight. For an object of mass $$$m$$$ and weight $$$W$$$ , the gravitational field strength $$$g$$$ is:

g = \frac{W}{m}

Weight is measured in newtons ( $\mathrm{N}$ ), and mass is measured in kilograms ( $\mathrm{kg}$ ). Gravitational field strength is therefore measured in newtons per kilogram ( $\mathrm{N/kg}$ ).

Calculating weight or mass

The relationship can be rearranged depending on which quantity is unknown:

W = mg \qquad \text{and} \qquad m = \frac{W}{g}

For example, at a location where $g = 10\ \mathrm{N/kg}$ , an object of mass $2\ \mathrm{kg}$ has a weight of $2 \times 10 = 20\ \mathrm{N}$ .

Gravitational field strength and free fall

Gravitational field strength is equal to the acceleration of free fall at the same location. Free fall is motion under gravity alone, so air resistance is neglected. A field strength of $10\ \mathrm{N/kg}$ corresponds to a free-fall acceleration of $10\ \mathrm{m/s^2}$ . The units $\mathrm{N/kg}$ and $\mathrm{m/s^2}$ are equivalent.