Forces in Action: Moments, Hooke's Law & Stopping Distances

Turning Forces and the Moment of a Force

When you push a door, you instinctively push at the handle, far from the hinge. Pushing near the hinge barely works. This everyday fact is the heart of moments: a force can make an object turn, and how strongly it turns depends not just on the size of the force but on where it acts.

The moment of a force is the turning effect produced about a pivot.

$$moment = force \times perpendicular\ distance\ from\ the\ pivot$$

Force is in newtons (N), distance in metres (m), so the moment is measured in newton metres (N m).

Key terms

Pivot (fulcrum) — the fixed point about which an object turns.

Moment — the turning effect of a force, equal to force times perpendicular distance from the pivot.

Perpendicular distance — the shortest (at 90°) distance between the line of the force and the pivot.

The word perpendicular matters. If a force is applied at an angle, only the part acting at right angles to the lever arm produces the full turning effect — always use the perpendicular distance, measured straight from the pivot to the line of action of the force.

The Principle of Moments

Many objects are in equilibrium — balanced and not turning. For an object balanced on a pivot, the principle of moments states:

Key terms

Principle of moments — when an object is in equilibrium, the total clockwise moment about any pivot equals the total anticlockwise moment about that pivot.

$$\text{total clockwise moment} = \text{total anticlockwise moment}$$

A lever uses this principle to multiply force. A small force acting far from the pivot can balance (or lift) a large force acting close to the pivot. Crowbars, spanners, scissors, wheelbarrows and seesaws are all levers.

Worked example

A uniform seesaw is balanced on a central pivot. A child of weight 300 N sits 2 m from the pivot on the right. Where must a child of weight 200 N sit on the left to balance it?

Clockwise moment (300 N child) $= 300 \times 2 = 600$ N m.

For balance, the anticlockwise moment must also be 600 N m.

$200 \times d = 600$, so $d = 600 \div 200 = 3$ m.

Exam tip

Always show the equation clockwise = anticlockwise and substitute numbers before rearranging. List each moment as force × distance. Marks are given for correct working even if the final number slips.

Centre of Gravity and Stability

The weight of an object seems to act from a single point called the centre of gravity (the point where all the object's weight appears to act). For a regular, uniform object — a ruler, a ball, a beam — it sits at the geometric centre.

The position of the centre of gravity controls stability:

An object is stable when its centre of gravity is low and its base is wide. A racing car is hard to tip over for exactly this reason.
An object topples when its centre of gravity passes outside the edge of its base. Until that point it rocks back; beyond it, the weight produces a moment that tips it right over.
A tall, narrow object (a double-decker bus, a wine glass) has a higher centre of gravity and tips more easily.

Real world

Buses are tested by tilting them on a ramp. A double-decker must not topple even when tilted to a steep angle with the upper deck loaded. Keeping heavy components (engine, battery) low keeps the centre of gravity down and the bus stable.

Hooke's Law

Stretch a spring gently and it gets longer. Stretch it twice as hard and it gets twice as long. This proportional behaviour is Hooke's law:

$$F = k\,x$$

$F$ = force applied, in newtons (N)
$x$ = extension (the increase in length, not the total length), in metres (m)
$k$ = the spring constant, in newtons per metre (N/m) — a measure of stiffness. A stiff spring has a large $k$.

Key terms

Extension — the increase in length compared with the original (natural) length: $x = \text{stretched length} - \text{original length}$.

Spring constant ($k$) — the force needed to produce unit extension; stiffer springs have larger $k$.

Limit of proportionality — the point beyond which extension is no longer proportional to force, and the line on the graph stops being straight.

Force–Extension Graphs

Plotting force against extension gives a straight line through the origin — as long as Hooke's law holds. The gradient of that line equals the spring constant $k$.

Beyond a certain force, the line bends. This point is the limit of proportionality. Stretch even further and the spring is permanently deformed — it will not return to its original length when the force is removed. Below that limit the spring shows elastic behaviour (it returns to its original shape when the load is removed).

The Spring Experiment

A standard practical investigates Hooke's law:

1. Hang a spring from a clamp stand and record its natural length with a metre ruler.
2. Add a known weight (for example a 1 N mass hanger) and measure the new length.
3. Calculate the extension by subtracting the natural length.
4. Add weights one at a time, recording the length each time.
5. Plot a graph of force (y-axis) against extension (x-axis).

The straight portion confirms Hooke's law; its gradient gives $k$. The point where the line curves is the limit of proportionality.

Watch out

Plot extension, not total length. A common error is recording the spring's full length and forgetting to subtract the original. Always: extension = stretched length − natural length.

Friction

Friction is a force that opposes motion between two surfaces in contact. It always acts in the opposite direction to movement (or attempted movement). Friction can be a nuisance — it wastes energy as heat and wears parts down — but it is also essential: without it, tyres could not grip the road, brakes could not slow a car, and you could not walk.

Friction depends on the surfaces: rough surfaces and firmly pressed-together surfaces produce more friction; smooth or lubricated surfaces produce less.

Stopping Distances

When a driver spots a hazard, the car does not stop instantly. The total stopping distance is made of two parts:

$$\text{stopping distance} = \text{thinking distance} + \text{braking distance}$$

Thinking distance — the distance travelled during the driver's reaction time, before the brakes are applied.
Braking distance — the distance travelled while the brakes are slowing the car to a stop.

Watch out

A common exam trap: drugs, alcohol and tiredness increase the thinking distance only — they do not change how the brakes work. Road and vehicle conditions (ice, worn tyres, faulty brakes) affect the braking distance only. Speed increases both.

Exam tip

Braking distance does not increase in proportion to speed — it increases much faster. Doubling the speed roughly quadruples the braking distance, because the kinetic energy that the brakes must remove depends on speed squared. Examiners love this point.

A larger braking distance means the brakes must do more work, transferring more kinetic energy into heat in the brake pads and discs. This is why brakes get hot, and why braking from high speed on a wet road is so dangerous.