What you'll learn
Forces is the largest unit in AQA GCSE Combined Science: Trilogy physics and the one that most rewards careful working. It begins with the distinction between scalar and vector quantities, moves through the effects of forces on stationary and moving objects, and ends with motion, Newton's laws and the physics of stopping a car. By the end of this unit you should be able to distinguish scalars from vectors, calculate weight and work done, apply Hooke's law and calculate the energy stored in a spring, calculate speed and acceleration, interpret distance–time and velocity–time graphs including finding a gradient and an area, state and apply all three of Newton's laws, explain terminal velocity, and analyse stopping distance in terms of thinking distance and braking distance. This unit is assessed on Physics Paper 2 and includes the required practicals on force and extension and on acceleration.
Key terms and definitions
Scalar quantity — a quantity with magnitude only, such as speed, distance, mass or energy
Vector quantity — a quantity with both magnitude and direction, such as velocity, displacement, force, weight and acceleration
Contact force — a force acting between objects that are physically touching, such as friction, air resistance, tension and the normal contact force
Non-contact force — a force acting between objects that are separated, such as gravitational, electrostatic and magnetic force
Weight — the force acting on an object due to gravity, equal to mass multiplied by gravitational field strength
Resultant force — the single force that has the same effect as all the forces acting on an object combined
Work done — energy transferred when a force moves an object along the line of action of the force
Limit of proportionality — the point beyond which extension is no longer directly proportional to the force applied
Inertia — the tendency of an object to continue in its state of rest or of uniform motion
Terminal velocity — the constant velocity reached by a falling object when the resultant force on it is zero
Stopping distance — the sum of the thinking distance and the braking distance
Core concepts
Scalars, vectors and types of force
A scalar has magnitude only; a vector has magnitude and direction. The pairs that matter are distance and displacement, and speed and velocity. Distance and speed are scalars; displacement and velocity are vectors. This is why a car driving in a circle can have a constant speed but a continuously changing velocity.
A force is a push or pull on an object that results from its interaction with another object. Forces are vectors, and they are either contact or non-contact.
Weight and mass
Mass is a scalar measured in kilograms and is a property of the object alone. Weight is a vector force measured in newtons, acting straight downwards towards the centre of the Earth.
Weight equals mass multiplied by gravitational field strength. On the Earth's surface the gravitational field strength is about 9.8 newtons per kilogram, so a 60 kilogram person weighs about 588 newtons.
Weight and mass are directly proportional, which is why a set of scales calibrated on Earth would give a different reading on the Moon even though the mass is unchanged. Weight is measured using a calibrated spring balance, also called a newtonmeter.
Resultant forces and free body diagrams
A number of forces acting on an object may be replaced by a single resultant force with the same effect. Forces acting along the same line are combined by adding those in one direction and subtracting those in the other.
If the resultant force is zero the forces are balanced, and the object stays at rest or continues at constant velocity. If the resultant force is not zero the object accelerates in the direction of the resultant.
Work done
When a force causes an object to move through a distance, work is done and energy is transferred. Work done equals force multiplied by distance moved along the line of action of the force, with force in newtons, distance in metres and work in joules. One joule of work is done when a force of one newton causes a displacement of one metre.
Work done against frictional forces acting on an object causes a rise in temperature of the object, which is why brakes get hot and why rubbing hands together warms them.
Forces and elasticity
To change the shape of a stationary object, more than one force has to be applied. An object has been elastically deformed if it returns to its original shape when the forces are removed, and inelastically deformed if it does not.
For an elastic object, the extension is directly proportional to the force applied, provided the limit of proportionality is not exceeded. Force equals spring constant multiplied by extension, with the spring constant in newtons per metre and extension in metres.
A force–extension graph is therefore a straight line through the origin up to the limit of proportionality, and curves away beyond it. The gradient of the straight section gives the spring constant, and the area under the line gives the work done in stretching the spring.
The extension must be measured from the original unstretched length. Using the total length instead of the extension is one of the most common errors in the whole unit.
Speed, velocity and acceleration
Distance is a scalar and displacement a vector; speed is a scalar and velocity a vector. Speed equals distance divided by time, with distance in metres, time in seconds and speed in metres per second.
Typical everyday speeds that are worth knowing are about 1.5 metres per second for walking, 3 metres per second for running and 6 metres per second for cycling. The speed of sound in air is about 330 metres per second.
Acceleration is the change in velocity divided by the time taken, measured in metres per second squared. An object slowing down has a negative acceleration, often called deceleration.
There is also an equation relating final velocity, initial velocity, acceleration and distance: the final velocity squared minus the initial velocity squared equals two multiplied by acceleration multiplied by distance. It is useful whenever time is not given.
Near the Earth's surface, any object falling freely accelerates at about 9.8 metres per second squared.
Motion graphs
A distance–time graph has distance on the vertical axis and time on the horizontal. A horizontal line means the object is stationary. A straight sloping line means constant speed, and the gradient gives that speed. A curve means the speed is changing, and the speed at a moment is found by drawing a tangent and calculating its gradient.
A velocity–time graph has velocity on the vertical axis. A horizontal line means constant velocity. A sloping line means acceleration, and the gradient gives the acceleration. Crucially, the area under a velocity–time graph gives the distance travelled, which is found by splitting the shape into rectangles and triangles.
Confusing the two graph types is the single largest source of lost marks in this unit. Always read the vertical axis label before interpreting.
Newton's laws
Newton's first law states that an object remains at rest, or continues at constant velocity in a straight line, unless acted on by a resultant force. The tendency of an object to resist a change in its motion is its inertia.
Newton's second law states that the acceleration of an object is proportional to the resultant force and inversely proportional to its mass, giving resultant force equals mass multiplied by acceleration. Inertial mass is a measure of how difficult it is to change the velocity of an object, and is defined as force divided by acceleration.
Newton's third law states that whenever two objects interact, the forces they exert on each other are equal and opposite. The two forces in such a pair always act on different objects, which is why they do not cancel out.
Terminal velocity
When an object falls through a fluid, it initially accelerates because its weight is greater than the drag force. As it speeds up, the drag force increases. Eventually the drag force equals the weight, the resultant force becomes zero, and by Newton's first law the object continues at a constant velocity: its terminal velocity.
A velocity–time graph for such a fall starts steep, becomes progressively shallower as the resultant force decreases, and finally levels off horizontally.
Stopping distance
The stopping distance of a vehicle is the sum of the thinking distance, travelled during the driver's reaction time, and the braking distance, travelled while the brakes are applied.
Thinking distance is increased by anything that lengthens reaction time: tiredness, alcohol, drugs and distractions. Braking distance is increased by poor road conditions such as ice, rain or leaves, and by poor vehicle condition such as worn brakes or worn tyres. Both increase with speed.
When brakes are applied, work done by the friction force between the brakes and the wheel reduces the kinetic energy of the vehicle and increases the temperature of the brakes. A greater speed requires a greater braking force to stop the vehicle in the same distance, and large decelerations may cause the brakes to overheat or the driver to lose control.
Worked examples
Example 1: Calculating a spring constant (3 marks)
A spring extends by 0.08 metres when a force of 12 newtons is applied, within the limit of proportionality. Calculate the spring constant.
Force equals spring constant multiplied by extension, so the spring constant equals force divided by extension. That is 12 divided by 0.08, which gives 150 newtons per metre.
Example 2: Reading a velocity–time graph (4 marks)
A velocity–time graph shows a car accelerating uniformly from 0 to 20 metres per second in 8 seconds, then travelling at 20 metres per second for 12 seconds. Calculate the acceleration and the total distance travelled.
The acceleration is the change in velocity divided by time, which is 20 divided by 8, giving 2.5 metres per second squared. The distance is the area under the graph. The first section is a triangle of area one half multiplied by 8 multiplied by 20, which is 80 metres. The second is a rectangle of area 12 multiplied by 20, which is 240 metres. The total distance is 80 plus 240, giving 320 metres.
Example 3: Explaining terminal velocity (4 marks)
Explain why a skydiver reaches a terminal velocity.
At the start of the fall the skydiver's weight is much greater than the air resistance, so there is a large resultant force downwards and the skydiver accelerates. As the speed increases, the air resistance increases, so the resultant force decreases and the acceleration falls. Eventually the air resistance becomes equal to the weight, the resultant force is zero, and by Newton's first law the skydiver continues to fall at a constant velocity, the terminal velocity.
Common mistakes and how to avoid them
The most damaging error in this unit is treating a distance–time graph as a velocity–time graph. On a distance–time graph a horizontal line means stationary; on a velocity–time graph it means constant speed. Read the axis label first.
Students routinely use total length instead of extension in Hooke's law. Extension is the increase from the original length, so subtract before substituting.
Another frequent slip is confusing mass and weight, or giving weight in kilograms. Weight is a force in newtons.
In Newton's third law questions, many answers claim the equal and opposite forces cancel. They act on different objects, so they cannot cancel each other.
Finally, stopping distance answers often give only factors affecting braking distance. Thinking distance and braking distance are affected by different things, and questions usually award marks for both.
Exam technique for "Physics: Forces"
Draw a diagram with the forces marked whenever a question describes a physical situation. It costs little time and makes the resultant force obvious.
For graph questions, decide first whether you need a gradient or an area. Gradient of distance–time gives speed; gradient of velocity–time gives acceleration; area under velocity–time gives distance. Nothing else is required.
Show unit conversions explicitly. Speeds given in kilometres per hour and distances in centimetres are common in this unit, and unconverted values produce answers that are wrong by a factor of 1,000 or more.
For the required practical on acceleration, be ready to identify the independent variable as the force applied or the mass of the trolley, the dependent variable as the acceleration, and to explain how light gates or a timer measure it.
Quick revision summary
Scalars have magnitude only and vectors have magnitude and direction. Weight equals mass times gravitational field strength, about 9.8 newtons per kilogram on Earth. A zero resultant force means rest or constant velocity; a non-zero resultant produces acceleration. Work done equals force times distance, and work against friction raises temperature. Force equals spring constant times extension up to the limit of proportionality, with the gradient of a force–extension graph giving the spring constant and the area giving the energy stored. Speed equals distance divided by time and acceleration equals change in velocity divided by time. On a distance–time graph the gradient is speed; on a velocity–time graph the gradient is acceleration and the area is distance. Newton's laws cover constant velocity without resultant force, resultant force equals mass times acceleration, and equal and opposite forces on different objects. Terminal velocity is reached when drag equals weight. Stopping distance is thinking distance plus braking distance, both increasing with speed.