Forces — AQA Combined Science: Trilogy
Forces is a large unit covering scalars and vectors, types of force, motion, Newton's laws, stopping distances and momentum.
Scalars and vectors
- Scalar quantities have size (magnitude) only — e.g. speed, distance, mass, energy, temperature.
- Vector quantities have magnitude and direction — e.g. velocity, displacement, force, acceleration. Vectors are drawn as arrows.
Types of force
- Contact forces — objects must touch (e.g. friction, air resistance, tension, normal contact force).
- Non-contact forces — act at a distance (e.g. gravity, magnetic, electrostatic).
A force is a push or pull on an object due to its interaction with another object.
Weight and mass
- Mass is the amount of matter (kg) and is constant.
- Weight is the force of gravity on an object (N): $$W = m \times g$$ (g ≈ 9.8 N/kg on Earth). Weight depends on the gravitational field strength, so it changes on the Moon.
Resultant force
When several forces act on an object, they can be replaced by a single resultant force. If the resultant force is zero, the object is in equilibrium. Free body diagrams show the forces acting on an object.
Work done
When a force moves an object, work is done and energy is transferred: $$W = F \times d$$ (work in joules = force × distance moved in the direction of the force). Work done against friction transfers energy to thermal stores (things heat up).
Forces and elasticity
Stretching, bending or compressing an object requires more than one force. For an elastic object (e.g. a spring), Hooke's law applies up to the limit of proportionality: $$F = k \times e$$ (force = spring constant × extension). The extension is directly proportional to the force, giving a straight-line graph until the limit, after which it curves.
Required practical: investigating the relationship between force and extension of a spring.
Motion
- Distance is scalar; displacement is a vector.
- Speed is scalar; velocity is speed in a given direction.
$$\text{speed} = \frac{\text{distance}}{\text{time}}$$
Acceleration: $$a = \frac{\Delta v}{t}$$ (change in velocity ÷ time). Use the equation $v^2 - u^2 = 2as$ for uniform acceleration.
Motion graphs
- Distance–time graph: the gradient is the speed. A curved line means changing speed.
- Velocity–time graph: the gradient is the acceleration; the area under the line is the distance travelled.
Newton's laws of motion
- First law: an object stays at rest, or moves at constant velocity, unless acted on by a resultant force. (Constant velocity needs zero resultant force.)
- Second law: the acceleration is proportional to the resultant force and inversely proportional to the mass: $$F = m \times a$$
- Third law: when two objects interact, they exert equal and opposite forces on each other.
Inertia is the tendency of an object to stay in its state of rest or uniform motion; inertial mass measures how hard it is to change an object's velocity.
Terminal velocity
A falling object accelerates due to gravity, but air resistance increases with speed. When air resistance equals the weight, the resultant force is zero and the object falls at a constant terminal velocity.
Stopping distances
Stopping distance = thinking distance + braking distance.
- Thinking distance — distance travelled during the driver's reaction time. Increased by tiredness, alcohol, drugs and distractions.
- Braking distance — distance travelled while braking. Increased by higher speed, poor road/weather conditions and worn brakes/tyres.
Greater speed increases both, but braking distance increases more sharply (with the square of speed). Braking hard transfers a lot of kinetic energy to the brakes, which can overheat.
Momentum (Higher Tier)
Momentum is a vector: $$p = m \times v$$ (momentum = mass × velocity, in kg m/s).
In a closed system, the total momentum before an event equals the total momentum after — the conservation of momentum. This applies to collisions and explosions.
Exam tips
- Classify quantities as scalar or vector confidently.
- Learn W = mg, W = Fd, F = ke, a = Δv/t and F = ma, and practise rearranging.
- For velocity–time graphs: gradient = acceleration, area = distance.
- Explain terminal velocity in terms of balanced forces.
- Stopping distance: link thinking distance to reaction time and braking distance to speed/conditions.