# Mass

## Key Stage 2

### Meaning

Mass is the amount of stuff an object or material is made of.

Mass can be measured using a measuring scale.
Mass is measured in grams and kilograms.

## Note to Teachers

Students are frequently confused by the difference between mass and weight. This is in part due to the terms being used interchangeably during KS1 maths. It is also due to grams and kilograms being falsely referred to as weight in common parlance. The conceptual difference that mass is 'the amount of stuff in an object' and weight is 'the amount of force pulling an object down' should not be too complicated for a student. However, breaking the habit of using the words interchangeably proves challenging. Teachers should do their best to say 'mass' whenever they are talking about grams or kilograms and say Newtons, stone, pounds or ounces when talking about weight. A useful rule is to remember than on Earth 1kg weighs 10 Newtons. This gives an easy conversion when you want to talk about weight instead of mass. This is different in space where; on the moon 1kg weighs 1.6 Newtons and on Jupiter 1kg weighs 25 Newtons.

## Key Stage 3

### Meaning

Mass is the amount of matter that something is made of, measured in kilograms.

Mass can be measured using a measuring scale.
The more mass an object has, the harder it is to accelerate the object.

The units of mass you should be able to use are:

## Key Stage 4 Foundation

### Meaning

Mass is the amount of matter that something is made of, measured in kilograms.

Mass can be measured using a measuring scale or Electronic Balance.
The SI Unit of mass is the kilogram.
Mass is a scalar quantity as it has magnitude but does not have a direction.
The more mass an object has, the harder it is to accelerate the object.

The units of mass you should be able to use are:

## Key Stage 4 Higher

### Meaning

Inertial mass is $$mass = \frac{Force}{acceleration}$$; the ratio of force to the acceleration of an object.

Mass is the resistance of an object to being accelerated. The greater the mass the more force is needed to accelerate it.
Mass can be measured using a measuring scale or Electronic Balance.
The SI Unit of mass is the kilogram.
Mass is a scalar quantity as it has magnitude but does not have a direction.

The units of mass you should be able to use are:

### Equation

NB: You need to remember this equation.

Inertial Mass = (Resultant Force)/(Acceleration)

$$m = \frac{Force}{acceleration}$$

Where

$$m$$ = The Inertial Mass of the object.

$$F$$ = The Resultant Force on the object.

$$a$$ = The acceleration of the object.

### Example Calculations

#### Finding the Inertial Mass given the Force and Acceleration

 An object is subjected to a resultant force of 92N and accelerates at a rate of 0.42m/s/s. Calculate the inertial mass of the object correct to two significant figures. The brakes of a car provide a force of 12kN and are able to decelerate it at a rate of 8.7m/s/s. Calculate the intertial mass of the car correct to two significant figures. 1. State the known quantities a = 0.42m/s/s F = 92N 1. State the known quantities a = 8.7m/s/s F = 12kN = 12 x 103N 2. Substitute the numbers into the equation and solve. $$m= \frac{F}{a}$$ $$m = \frac{92}{0.42}$$ $$m = 219.047619kg$$ $$m \approx 220kg$$ 2. Substitute the numbers into the equation and solve. $$m= \frac{F}{a}$$ $$m = \frac{12 \times 10^3}{8.7}$$ $$m = 1379.31034kg$$ $$m \approx 1400kg$$