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Physics · Forces

Pressure in a fluid

Use \(p = F \div A\), explain how pressure in fluids acts at right angles to surfaces, and explain everyday examples of pressure.

  • 6 key terms
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Teacher resources

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Student handouts

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Warm-up

Answer each one, then check.

  1. 1

    What is area?

    Show answerHide answer

    The amount of surface

  2. 2

    What is the unit of area?

    Show answerHide answer

    Square metres (m²)

  3. 3

    What is a fluid?

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    A liquid or a gas

  4. 4

    What is the unit of force?

    Show answerHide answer

    Newton

  5. 5

    What is the unit of pressure?

    Show answerHide answer

    Pascal (Pa)

Learning Objectives

  1. 1Define pressure and recall that a fluid can be a liquid or a gas.
  2. 2Recall and apply \(p = F \div A\).
  3. 3Explain that pressure in a fluid causes a force at right angles to any surface.
  4. 4Explain examples where force is spread over a large or small area.

PRESSURE

pressure \(=\) force normal to a surface \(\div\) area of that surface \(p = \dfrac{F}{A}\)

Pressure is in pascals (Pa), force in newtons (N) and area in square metres (m²). 1 Pa = 1 N/m².

Calculating Pressure

A person of weight 600 N stands on an area of 0.04 m². Calculate the pressure on the ground.

Show the solutionHide the solution
  1. 1 Write the equation \(p = F \div A\)
  2. 2 Substitute \(p = 600 \div 0.04\)
  3. 3 Answer \(p = 15\,000\) Pa

Answer15 000 Pa

Finding the Force

A pressure of 2000 Pa acts on a surface of area 0.50 m². Calculate the force.

Show the solutionHide the solution
  1. 1 Rearrange \(F = pA\)
  2. 2 Substitute \(F = 2000 \times 0.50\)
  3. 3 Answer \(F = 1000\) N

Answer1000 N

Explaining Everyday Examples

Explain why a sharp knife cuts better than a blunt one.

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  1. 1 Same force The same force is applied to both
  2. 2 Sharp edge Has a very small area
  3. 3 Pressure A small area gives a large pressure, so it cuts

AnswerThe sharp knife has a smaller area, so for the same force it exerts a higher pressure.

Pressure in Fluids

Liquids and gases.

  • Direction

    Pressure in a fluid causes a force normal (at right angles) to any surface.

  • Gases

    Produced by collisions of particles with surfaces.

  • Liquids

    Particles collide with the container walls in all directions.

  • Uses

    Tyres, hydraulics and sealed containers use fluid pressure.

Shoe Pressure

A 500 N person wears stiletto heels of total area 0.0004 m² and then flat shoes of area 0.04 m². Calculate the pressure each exerts and explain which damages a floor.

1. Calculate each pressure.

2. Compare.

A good answer shows: Heels: 500 ÷ 0.0004 = 1 250 000 Pa. Flat: 500 ÷ 0.04 = 12 500 Pa. The heels exert 100 times more pressure, so they damage the floor.

Can I...?

  1. 1Define pressure.
  2. 2Use \(p = F \div A\).
  3. 3Rearrange for force or area.
  4. 4Convert cm² to m².
  5. 5Explain sharp and blunt objects.
  6. 6Explain wide tyres.
  7. 7State the direction of fluid pressure.
  8. 8Give the unit.

Summary & Exam Focus

  • \(p = F \div A\).
  • Smaller area, larger pressure.
  • Fluid pressure acts at right angles to surfaces.
  • 1 Pa = 1 N/m².

Exam focus

A person of weight 600 N stands on 0.04 m² of ground. Calculate the pressure. (2 marks) (2 marks)

Divide force by area.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Pressure
Force per unit area.
Pascal
The unit of pressure; 1 N/m².
Fluid
A liquid or a gas.
Normal
At right angles to a surface.
Area
The size of a surface.
Force
A push or pull.

Questions and answers

10 questions set on this lesson, with the mark schemes and model answers open.

1. Exam question Calculate 2 marks Easier

A person weighs 600 N and stands on an area of 0.04 m². Calculate the pressure on the ground. Use the equation: pressure = force ÷ area

Mark scheme — 2 marks available

  • Correct substitution — 1 mark
  • 15 000 Pa — 1 mark

Model answer

\(600 \div 0.04 = 15\,000\) Pa

2. Exam question Explain 2 marks Easier

A nail has a sharp point. Explain why it is easier to push into wood than a blunt object.

Mark scheme — 2 marks available

  • Small area — 1 mark
  • Greater pressure for the same force — 1 mark

Model answer

The point has a small area, so the same force gives a greater pressure.

3. Exam question Explain 3 marks Easier

A tractor with wide tyres does not sink into soft ground as much as a car with narrow tyres of the same weight. Explain why.

Mark scheme — 3 marks available

  • Weight is the same — 1 mark
  • Larger area — 1 mark
  • Smaller pressure — 1 mark

Model answer

The wide tyres spread the weight over a larger area, so the pressure on the ground is smaller.

4. Exam question Calculate 3 marks Easier

A pressure of 2000 Pa acts on a surface of area 0.50 m². Calculate the force on the surface.

Mark scheme — 3 marks available

  • Rearranges to F = pA — 1 mark
  • Correct substitution — 1 mark
  • 1000 N — 1 mark

Model answer

\(F = pA = 2000 \times 0.50 = 1000\) N

5. Exam question Calculate 4 marks Easier

A 500 N person wears shoes with a total area of 0.0004 m² on a floor. Calculate the pressure. Then state how many times greater it is than the pressure from flat shoes of area 0.04 m².

Mark scheme — 4 marks available

  • 1 250 000 Pa — 1 mark
  • 12 500 Pa — 1 mark
  • Ratio 100 — 1 mark
  • States 100 times greater — 1 mark

Model answer

\(500 \div 0.0004 = 1\,250\,000\) Pa; \(500 \div 0.04 = 12\,500\) Pa; the pressure is 100 times greater.

6. Multiple choice 1 mark Easier

Pressure is...

  1. A force times area
  2. B area per force
  3. C mass per volume
  4. D force per unit area Correct

Why: p = F ÷ A.

7. Multiple choice 1 mark Core

The unit of pressure is...

  1. A pascal Correct
  2. B newton
  3. C joule
  4. D watt

Why: 1 Pa = 1 N/m².

8. Multiple choice 1 mark Core

A smaller area with the same force gives...

  1. A a smaller pressure
  2. B a greater pressure Correct
  3. C the same pressure
  4. D no pressure

Why: p = F ÷ A.

9. Multiple choice 1 mark Core

100 N on 2 m² gives...

  1. A 200 Pa
  2. B 0.02 Pa
  3. C 50 Pa Correct
  4. D 102 Pa

Why: 100 ÷ 2.

10. Multiple choice 1 mark Stretch

A fluid is...

  1. A a solid
  2. B a force
  3. C a scalar
  4. D a liquid or a gas Correct

Why: Both can flow.