Forces in action — OCR GCSE Physics

Stretching a spring stores elastic potential energy. The energy transferred is E = ½ × k × e², where E is energy in joules (J), k is the spring constant in N/m and e is the extension in metres. The extension is squared, so it must be in metres before squaring; 4 cm becomes 0.04 m, and 0.04² = 0.0016 m². A spring with k = 300 N/m stretched by 0.02 m stores E = ½ × 300 × 0.0004 = 0.06 J. Because of the square, doubling the extension quadruples the energy stored. The formula applies within the elastic limit, where the spring returns to its original shape.

Weight is the gravitational force on a mass, and the equation W = m × g links them. Mass in kilograms measures how much matter is present; gravitational field strength g in newtons per kilogram tells you the force on each kilogram. On Earth g is about 9.8 N/kg, so a 5 kg bag has a weight of 5 × 9.8 = 49 N. On the Moon g is about 1.6 N/kg, so the same 5 kg bag weighs 5 × 1.6 = 8 N while its mass stays 5 kg. To apply the equation, identify m and g, multiply, and attach the unit N. To rearrange, divide weight by g to find mass, or divide weight by mass to find g. Check that the unit N/kg is equivalent to m/s², since a newton per kilogram is the same as a metre per second squared.

Gravitational potential energy (GPE) is the energy stored when a mass is raised against gravity. The equation is GPE = m × g × h, with energy in joules, mass in kilograms, gravitational field strength in newtons per kilogram and height in metres. Lifting a 2 kg book by 3 m on Earth stores 2 × 9.8 × 3 = 58.8 J. Height must be the vertical change, so a slope distance is not the height unless it is the vertical rise. To rearrange, divide GPE by (m × g) to find height, or by (g × h) to find mass. When an object falls, the stored GPE transfers to kinetic energy, so the same equation can find the energy released. Check units carefully: convert centimetres to metres and grams to kilograms before substituting.

Pressure measures how concentrated a force is over a surface. The equation is p = F/A, where F is the force acting perpendicular (normal) to the surface, in newtons, and A is the area of that surface in square metres. The result is in pascals, where 1 Pa = 1 N/m². A force of 60 N spread over 0.03 m² gives p = 60 ÷ 0.03 = 2000 Pa. Only the normal component counts, so a force acting along the surface contributes nothing to pressure. A smaller area for the same force raises the pressure, which is why a sharp point or narrow heel presses harder. Convert areas to m² first: 1 cm² = 1 × 10⁻⁴ m², so 250 cm² = 0.025 m². This content appears only in the physics separate science qualification.

A moment measures the turning effect of a force about a pivot. The equation is M = F × d, where F is the force in newtons and d is the perpendicular distance in metres from the pivot to the line of action of the force, measured normal to the force's direction. The moment is in newton metres (N m). A 20 N force applied 0.5 m from a pivot, perpendicular to the lever, gives M = 20 × 0.5 = 10 N m. If the force acts at an angle, use only the perpendicular distance, not the slant length along the lever. Doubling either the force or the perpendicular distance doubles the moment. Convert distances to metres first: 35 cm = 0.35 m. This content appears only in the physics separate science qualification.

A single force acting on an object does not stretch, bend or compress it; it simply accelerates the object in the direction of the force. To change shape, forces must act in opposing directions so that the object is pulled or pushed from more than one side. Stretching a spring means pulling each end outwards; compressing a spring means pushing each end inwards; bending a beam means applying forces that do not act along the same line. In each case the forces are applied at different points and are not balanced overall in the sense of producing no distortion, so the object deforms. Real-life examples include a gymnast's uneven bars bending under her weight and the reaction at the supports, a bridge deck flexing under traffic, and a rubber band stretched between two fingers.

When a stretching force is removed, an object may return to its original shape or stay permanently changed. Elastic deformation occurs when the object returns to its original length and shape once the stretching force is removed; the material behaves elastically, as a rubber band or a spring does within its elastic limit. Plastic deformation occurs when the object is permanently distorted and does not return to its original shape after the force is removed; a metal paperclip bent too far or a piece of plastic stretched beyond its limit shows plastic behaviour. The key distinction is reversibility: elastic deformation is reversible, plastic deformation is not. A material may behave elastically for small forces and plastically once the force exceeds its elastic limit.

For a spring or other simple elastic system, the extension grows as the applied force grows, provided the elastic limit is not exceeded. In this straight-line region the relationship is proportional: doubling the force doubles the extension, so force divided by extension stays constant and equals the spring constant k, with F = kx. A force–extension graph then plots as a straight line through the origin, and its gradient gives k. Beyond the elastic limit the line curves and the spring is permanently deformed, so the simple proportionality no longer holds. Learners should read values from such a graph, compare gradients and explain what a curved section shows.

A linear force–extension relationship gives a straight-line graph through the origin: equal increases in force produce equal increases in extension, so the ratio of force to extension is constant. A non-linear relationship gives a curved graph, so equal force steps produce unequal extension steps and the ratio changes as force rises. For a spring, the linear region holds below the elastic limit; beyond it the graph curves and the spring deforms permanently. Learners should distinguish the two by inspecting the shape of the graph, by testing whether the ratio stays constant, and by explaining what the curvature means physically rather than merely calling it 'not straight'.

In linear cases a spring stretches in proportion to the force applied, so a graph of force against extension is a straight line through the origin. The spring constant k measures stiffness and is found by rearranging F = kx to give k = F ÷ x, where F is the applied force in newtons and x is the extension in metres (final length minus original length). A spring needing 6 N to stretch 0.03 m has k = 6 ÷ 0.03 = 200 N/m. A stiffer spring needs more force for the same extension, so it has a larger k. Convert centimetres to metres before dividing, and remember that extension is the change in length, not the total length. The gradient of the force–extension line also equals k.

Stretching a spring transfers energy to it as elastic potential energy, and the work done equals the area under the force–extension graph. In linear cases the graph is a straight line from the origin, so the area is a triangle and the work done is W = ½Fx, where F is the final force in newtons and x the extension in metres. A spring stretched by 8 N through 0.05 m stores W = ½ × 8 × 0.05 = 0.2 J. The half appears because the force rises from zero to F as the spring stretches, so the average force is F ÷ 2. Convert extension to metres so the answer is in joules. Do not use W = Fx with the full force, which would overestimate the energy.

Every object with mass has a gravitational field, and that field always pulls other masses towards it rather than pushing them away. The field is strongest close to the object and weakens with distance. Field strength depends on how much mass the object contains: a more massive object produces a stronger field, so the Moon's pull on you is far weaker than the Earth's pull on you, and the Earth's pull is far weaker than the Sun's. In a multiple-choice question you may be asked which statement about the direction of the pull, or about how field strength changes with mass, is correct. Read each option and reject any that says gravity repels, that only large objects have a field, or that a small mass has the stronger field.

Weight is the force of gravity acting on an object, measured in newtons. You measure it with a newtonmeter, hanging the object from the hook so the spring stretches and the scale reads the force. Weight depends on mass and on the gravitational field strength g, the force per unit mass, through W = m × g. At the Earth's surface g is about 10 N/kg, so a 2 kg mass weighs 2 × 10 = 20 N. On the Moon g is smaller, so the same mass has a smaller weight while its mass stays the same. Mass is measured in kilograms with a balance; weight is a force measured in newtons.

Free fall means motion under gravity alone, with air resistance negligible. Near the Earth's surface the gravitational force on a mass m is W = m g, so the acceleration is a = W/m = m g / m = g. The mass cancels, so a heavy ball and a light ball dropped together accelerate at the same rate when air resistance is negligible. OCR expects you to recall the value of this acceleration: about 9.8 m/s², commonly rounded to 10 m/s² in calculations. Learn it as a magnitude with direction downward, and note that g is also the gravitational field strength in N/kg; 9.8 N/kg and 9.8 m/s² are numerically the same. A typical question asks which value matches free-fall acceleration, so distinguish it from 9.8 N (a force) and from speeds such as 9.8 m/s.

This criterion belongs to the physics separate science qualification only, so treat it as outside the combined-science route. The core relationship is weight equals mass times gravitational field strength, W = m g, where W is in newtons, m in kilograms and g in N/kg (about 9.8 N/kg near the Earth's surface). Because the equation is a product, doubling the mass doubles the weight at fixed g, and doubling g doubles the weight at fixed mass. Rearranged, m = W/g and g = W/m, so a measured weight and mass let you find g. On the Moon g is smaller, so the same mass has a smaller weight while its mass is unchanged. A typical multiple-choice task gives two of the three quantities and asks for the third, or asks how weight changes when mass or g changes.

A force applied away from a pivot can make an object turn. To describe such an example, name the object, state where the pivot is, state where the force acts and in which direction, then decide whether the turning effect is clockwise or anticlockwise. For a door, the pivot is at the hinge line; a push on the handle away from the hinge turns the door one way, and a push on the same handle from the other side turns it the opposite way. For a spanner on a nut, the pivot is the nut; pushing the end of the handle one way gives a clockwise turn and pushing the other way gives an anticlockwise turn. If two forces act, compare their turning effects to decide the resultant direction.

The moment of a force measures its turning effect about a pivot. Define it as the force multiplied by the perpendicular distance from the pivot to the line of action of the force, so moment = force × perpendicular distance, with the force in newtons and the distance in metres giving the moment in newton-metres (N m). To calculate, identify the pivot, find the perpendicular distance, then multiply. For a balanced object the principle of moments applies: the total clockwise moment about the pivot equals the total anticlockwise moment. For example, a 20 N force at 0.5 m gives 10 N m; if this balances an unknown force at 0.25 m on the other side, that force is 10 N m ÷ 0.25 m = 40 N.

A force applied at a distance from a pivot produces a turning effect, the moment, equal to force × perpendicular distance from the pivot. A lever transmits this rotational effect: a small effort applied far from the pivot balances a large load close to it, because the moments must match. The ratio of the effort arm to the load arm sets the force multiplication, so a lever with a long effort arm and short load arm turns a small force into a large one. Gears work the same way through their teeth: a small gear driving a large gear turns more slowly but with greater turning effect, and the ratio of teeth numbers gives the force (torque) multiplication. A larger driven gear multiplies force but reduces rotational speed, so energy is conserved while force and speed trade off.

A fluid is any substance that flows, so both gases and liquids count. Particles in a fluid move randomly and collide with the walls of their container or with any surface placed in the fluid. Each collision exerts a tiny force on the surface, and the combined effect of many collisions is a net force. Because the collisions are equally likely from every direction along the surface, this net force acts at right angles (perpendicular) to the surface, not along it. Pressure is this force per unit area, so a given pressure produces a larger force on a larger area. The same rule applies whether the fluid is a gas in a sealed container or a liquid in a tank, and the force always pushes perpendicular to whichever surface the fluid touches.

Pressure is force spread over the area in contact, so p = F ÷ A, with p in pascals (Pa), F in newtons (N) and A in square metres (m²). Rearranged, F = p × A and A = F ÷ p. A small area gives a large pressure for the same force, which is why a sharp pin pierces easily. A simple hydraulic system uses a liquid, which is virtually incompressible, to transmit pressure. Push a small piston of area A₁ with force F₁ and the pressure p = F₁ ÷ A₁ passes through the liquid to a larger piston of area A₂, giving F₂ = p × A₂. Because A₂ is larger, F₂ is larger than F₁, so a hydraulic system multiplies force, though the smaller piston must move further. This content appears only in the physics separate science qualification.