2.4 Pressure and pressure differences in fluids — Practise with help

Work each problem first. Open a hint only if you are stuck, and the full working only to check.

Warm-up: remember

Calculate the work done when a force of 60 N moves an object 5.0 m along the line of the force.
Write $1\,\text{m}^2$ in square centimetres.

Answers

$W = Fs = 60 \times 5.0 = 300\,\text{J}$ .
$1\,\text{m}^2 = 10000\,\text{cm}^2$ .

If question 2 went wrong, remember that the factor of 100 applies to both lengths, so it is squared: $100 \times 100 = 10000$ .

Practise with help

1. A force of 240 N acts on an area of 0.020 m². Calculate the pressure.

Hint

Pressure is the force normal to a surface divided by the area. The area is already in square metres.

Next step

Write $p = \dfrac{F}{A}$ , then divide 240 N by 0.020 m².

Full working

\begin{aligned} p &= \frac{F}{A} \\ &= \frac{240}{0.020} \\ &= 12000\,\text{Pa} \\ &= 1.2 \times 10^4\,\text{Pa} \end{aligned}

2. A pressure of 2500 Pa acts on an area of 0.48 m². Calculate the force normal to the surface.

Hint

Rearrange $p = \dfrac{F}{A}$ to make the force the subject.

Next step

Multiply the pressure by the area: $F = pA$ .

Full working

\begin{aligned} F &= p A \\ &= 2500 \times 0.48 \\ &= 1200\,\text{N} \\ &= 1.2 \times 10^3\,\text{N} \end{aligned}

3. Calculate the pressure due to a column of water 0.20 m high. The density of water is 1000 kg/m³ and $g = 9.8\,\text{N/kg}$ .

Hint

The pressure at a depth uses the height of the column, the density and $g$ .

Next step

Write $p = h\rho g$ , then put in $h = 0.20\,\text{m}$ , $\rho = 1000\,\text{kg/m}^3$ and $g = 9.8\,\text{N/kg}$ .

Full working

\begin{aligned} p &= h \rho g \\ &= 0.20 \times 1000 \times 9.8 \\ &= 1960\,\text{Pa} \\ &= 2.0 \times 10^3\,\text{Pa} \end{aligned}

4. Explain why atmospheric pressure decreases as the height above the ground increases.

Hint

Think about the air molecules above a surface, and about the weight of that air.

Next step

Say what happens to the number and the weight of the air molecules above the surface as the surface goes higher.

Full working

The atmosphere is a thin layer of air around the Earth. At a high surface there are fewer air molecules above it, so the weight of the air above is smaller. Fewer molecules collide with the surface, so the pressure is smaller. Atmospheric pressure therefore decreases as the height increases. This answer is a model answer for you to compare with your own wording.

5. A stone is lowered into a bucket of water. Explain why the stone feels an upward force, and state one factor that decides whether it floats.

Hint

Compare the depth of the top and the bottom of the stone.

Next step

Say which surface has the greater pressure, and what that difference does to the upward and downward forces.

Full working

The bottom of the stone is deeper than the top, so the pressure on the bottom is greater. The upward force on the bottom is larger than the downward force on the top, giving a resultant upward force called upthrust. The stone floats if its average density is less than the density of water, and sinks if its average density is greater. This answer is a model answer for you to compare with your own wording.