Define the moment of a force and apply the principle of moments, and define pressure and apply p = F/A including pressure in liquids

What this dot point is asking

SEAB wants you to define the moment of a force as its turning effect, to apply the principle of moments to a balanced beam, and to define pressure as force per unit area and apply $p = F/A$, including the way pressure increases with depth in a liquid. The arithmetic is simple multiplication and division; the marks come from the definitions and from choosing the perpendicular distance.

The answer

The moment of a force

A moment is the turning effect of a force about a pivot:

The unit is the newton metre ($\text{N m}$). A larger force or a longer distance gives a bigger turning effect, which is why a long spanner loosens a tight nut more easily than a short one.

The principle of moments

When an object is balanced (in equilibrium) and not turning, the total clockwise moment about any pivot equals the total anticlockwise moment:

This lets you find an unknown force or distance on a balanced beam such as a seesaw or a ruler balanced on a pivot.

Pressure

Pressure is the force acting per unit area:

The unit is the pascal ($\text{Pa}$), where $1\ \text{Pa} = 1\ \text{N/m}^2$. The same force gives a higher pressure over a smaller area, which is why a sharp knife cuts well and a drawing pin pushes in easily at its point.

Pressure in liquids

In a liquid the pressure increases with depth, because a deeper point has more liquid weighing down on it. The pressure due to a column of liquid is:

where $\rho$ is the density of the liquid, $g$ the gravitational field strength and $h$ the depth. Liquid pressure acts equally in all directions at a given depth.

Examples in context

Example 1. A wheelbarrow. The wheel acts as the pivot. By placing the load close to the wheel, its moment is small, so a modest lifting force at the far end of the long handles balances it. The handles give a large distance and therefore a large moment for little effort.

Example 2. Snowshoes and tractor tyres. Spreading weight over a large area lowers the pressure on soft ground, so the wearer or vehicle does not sink. The same weight on a small area, like a stiletto heel, gives a very high pressure that dents soft surfaces.

Try this

Q1. Define the moment of a force. [2 marks]

• Cue. The moment is the force multiplied by the perpendicular distance from the pivot to the line of action of the force.

Q2. A force of $50\ \text{N}$ acts on an area of $0.020\ \text{m}^2$. Find the pressure. [2 marks]

• Cue. $p = \dfrac{F}{A} = \dfrac{50}{0.020} = 2500\ \text{Pa}$.

Q3. Explain why pressure in a liquid increases with depth. [2 marks]

• Cue. A deeper point has a greater height of liquid above it, so more weight of liquid pushes down, giving a higher pressure.