**Units Used This Topic:**

**area **metre-squared (m^{2})

**density** kilogram/metre-cubed (kg/m^{3})

**distance** metre (m)

**extension **metre (m)

**force** Newton (N)

**gravitational field strength** Newton/kilogram (N/kg)

**height ** metre (m)

**mass** kilogram (kg)

**moment** Newton metre (Nm)

**pressure ** Pascal (Pa)

**spring constant** Newton/metre (N/m)

**weight** Newton (N)

**work done** Joule (J)

**acceleration** metre/second-squared (m/s^{2})

**momentum ** kilogram metre / second (kgm/s)

**speed ** metre/second (m/s)

**velocity** metre/second (m/s)

**time ** second (s)

**Scalar** quantities have magnitude only. Distance, speed and mass are scalar.

**Vector** quantities have magnitude and an associated direction. Displacement, velocity, force and acceleration are vector.

A vector quantity may be represented by an **arrow**. The length of the arrow represents the magnitude, and the direction of the arrow the direction of the vector quantity.

**Question:** Give the difference between a vector quantity and a scalar quantity.

both have magnitude; only a vector has direction

A force is a push or pull that acts on an object due to the interaction with another object. All forces between objects are either:

**contact forces**– the objects are physically touching, e.g. friction, air resistance, tension and normal contact force**non-contact forces**– the objects are physically separated, e.g. gravitational force, electrostatic force and magnetic force.

**Force is a vector **quantity.

When two objects touch, there is a normal contact force between them, perpendicular to the surface where they touch.

**Weight **is the force acting on an object due to gravity. The force of gravity close to the Earth is due to the gravitational field around the Earth.

The weight of an object depends on the gravitational field strength at the point where the object is.

The weight of an object can be calculated using the equation:** **

**weight = mass × gravitational field strength**

**Question:** A gymnast has a mass of 45 kg

gravitational field strength = 9.8 N/kg

Calculate the weight of the gymnast.

**weight = mass × gravitational field strength**

weight = 45 x 9.8

The weight of the gymnast is** 441 Newtons**

**Question**:An object has a weight of 6.4 N.

Calculate the mass of the object.

gravitational field strength = 9.8 N / kg

**weight = mass × gravitational field strength**

6.4 = mass x 9.8

mass = 6.4 / 9.8

The mass is **0.65 kg**

The weight of an object may be considered to act at a single point referred to as the object’s ‘**centre of mass**’.

Weight is measured using a **calibrated spring-balance** (a newtonmeter).

The weight of an object and the mass of an object are **directly proportional.**

## Directly Proportional

A directly proportional relationship is a straight line through the origin

The gradient is constant

The independent variable changes by the same value for each increment in the dependent variable

## Inversely Proportional

To show a graph is an inversely proportional relationship, at any point on the curve:

**independent variable x dependent variable = a constant**

## Resultant Forces

A number of forces acting on an object may be replaced by a single force that has the same effect as all the original forces acting together. This single force is called the **resultant force.**

The resultant force is the sum of all the individual forces acting on an object

learn this definition

## Names & Directions of Forces

## Resolving Forces

A single force can be **resolved** into two components acting at right angles to each other. The two component forces together have the same effect as the single force.

## Adding Forces

When more than one force is acting we can find the resultant force using a scale diagram. Draw the forces with a ruler and a protractor.

## Doing Work With Forces

When a force causes an object to move through a distance work is done on the object. So a force does work on an object when the force causes a displacement of the object.

The work done by a force on an object can be calculated using the equation:** **

**work done = force × distance moved along the line of action of the force**

**Question:** A cyclist used the brakes to slow down and stop the bicycle.

A constant braking force of 140 N stopped the bicycle in a distance of 24 m.

Calculate the work done by the braking force to stop the bicycle. Give the unit.

** work done = force × distance moved along the line of action of the force**

work done = 140 x 24

The work done is** 3360 Joules**

**Question:** A container was lifted a height of 14 m

The crane did 3 430 000 J of work on the container.

Calculate the force exerted by the crane on the container.

**work done = force × distance moved along the line of action of the force**

3430000 = force x 14

force = 3430000 / 14

The force is** 245000 Newtons**

One joule of work is done when a force of one newton causes a displacement of one metre. **1 joule = 1 newton-metre**

Work done against the frictional forces acting on an object causes a rise in the** temperature** of the object.

**Question: **A bicycle uses brakes to slow to a stop. Describe how the energy stores of the bicycle and the brakes change as the bike slows and stops. (2 marks)

The kinetic energy store of the bike will decrease

The thermal energy store of the brakes will increase