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11.1 Pressure and Surfaces

GCSE Physics · AQA · Chapter 11: Force and Pressure

A free GCSE Physics lesson for AQA (8463) from OBA School: what pressure is, the pascal, using p = F/A, and why contact area matters. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Describe pressure as the force acting normal (at right angles) to a surface per unit area
  • State that the unit of pressure is the pascal, where 1 Pa = 1 N/m², and use kPa and MPa
  • Use p = F/A and rearrange it to find a force or an area, converting cm² and mm² to m²
  • Explain why a small contact area gives a high pressure and a large contact area gives a low pressure
  • Describe how to measure the pressure a person exerts on the floor

Key words

  • Pressure: The force acting normal to a surface divided by the area of the surface it acts on.
  • Pascal (Pa): The unit of pressure. 1 Pa = 1 N/m², a force of one newton on each square metre.
  • Normal: At right angles (90°) to a surface.
  • Contact area: The area of the surface where two objects actually touch.
  • Fluid: A liquid or a gas. A fluid at rest pushes at right angles on every surface it touches.
  • Kilopascal (kPa): 1 kPa = 1000 Pa. Megapascal: 1 MPa = 1 000 000 Pa = 10⁶ Pa.

What is pressure?

Whenever one object pushes on another, the push is shared out over the area where they touch. Pressure tells you how concentrated that push is. The same force can have very different effects: spread over a large area it hardly dents the surface, but squeezed onto a tiny area it can pierce, cut or sink in.

Fluids (liquids and gases) also cause pressure. The particles of a fluid hit every surface they touch, so a fluid at rest exerts a force normal (at right angles) to any surface in contact with it – on the bottom, the sides and even the top of a submerged object.

Key fact: Pressure depends on two things: the size of the force (bigger force, bigger pressure) and the area it acts on (smaller area, bigger pressure).

The pressure equation

pressure = force normal to a surface ÷ area of that surface

p = F / A p in pascals (Pa), F in newtons (N), A in square metres (m²)

Rearranged: F = p × A A = F ÷ p

Worked example: pressure under a wardrobe

A wardrobe of weight 900 N stands on four small feet. Each foot has an area of 4.0 cm².
Total area = 4 × 4.0 = 16 cm² = 16 ÷ 10 000 = 0.0016 m²
p = F ÷ A = 900 ÷ 0.0016 = 562 500 Pa

Answer: about 5.6 × 10⁵ Pa (560 kPa)

Worked example: finding an area

A garden shed has a weight of 7200 N. The soil under it can take a pressure of up to 15 kPa without sinking.
Convert: 15 kPa = 15 000 Pa
A = F ÷ p = 7200 ÷ 15 000 = 0.48 m²

Answer: the base needs an area of at least 0.48 m²

Exam tip: If you are given a mass, change it into a weight first: W = m g with g = 9.8 N/kg. A 60 kg person has a weight of 60 × 9.8 = 588 N.

Units and area conversions

Areas in pressure questions are often given in cm² or mm². Because area is a length × a length, the conversion factor is squared too:

  • 1 m = 100 cm; Area 1 m² = 100 × 100 = 10 000 cm²; To get m² divide cm² by 10 000
  • 1 m = 1000 mm; Area 1 m² = 1000 × 1000 = 1 000 000 mm²; To get m² divide mm² by 1 000 000

Pressures are often large numbers, so prefixes are used: 1 kPa = 10³ Pa and 1 MPa = 10⁶ Pa. For example, 250 kPa = 250 000 Pa = 2.5 × 10⁵ Pa.

Worked example: a pressure in N/mm²

A needle presses on fabric with a force of 2.0 N. The tip has an area of 0.050 mm².
A = 0.050 ÷ 1 000 000 = 5.0 × 10⁻⁸ m²
p = 2.0 ÷ (5.0 × 10⁻⁸) = 4.0 × 10⁷ Pa

Answer: 4.0 × 10⁷ Pa (40 MPa) – a small force gives an enormous pressure

High pressure and low pressure in action

Designers choose the contact area to get the pressure they need. To cut or pierce, they make the area tiny. To stop things sinking or damaging a surface, they spread the force over a large area.

  • Sharp knife or scalpel; Contact area very small; Pressure very high; Why it is useful cuts with only a small force
  • Nail, drawing pin, needle; Contact area very small point; Pressure very high; Why it is useful pushes into wood, board or cloth
  • Snowshoes, skis; Contact area large; Pressure low; Why it is useful you do not sink into soft snow
  • Caterpillar tracks, wide tractor tyres; Contact area large; Pressure low; Why it is useful heavy vehicles cross mud or sand
  • Wide foundations, spreader plates; Contact area large; Pressure low; Why it is useful the ground does not give way

Measuring the pressure you put on the floor

1. Stand on squared paper (1 cm squares) and draw around both shoes.

2. Count the squares inside each outline. Count a square if more than half of it is inside; ignore it if less than half.

3. Add the two counts to get the contact area in cm², then divide by 10 000 to get m².

4. Find your mass on bathroom scales and work out your weight: W = m × 9.8 N/kg.

5. Pressure = weight ÷ area. Stand on one foot and the area halves, so the pressure doubles.

Worked example: a student’s pressure on the floor

Mass = 52 kg, so weight = 52 × 9.8 = 509.6 N
Squares counted: 148 for each shoe, so area = 296 cm² = 0.0296 m²
p = 509.6 ÷ 0.0296 = 17 216 Pa

Answer: about 17 kPa (2 significant figures)

Exam tip: Counting squares gives an estimate of area. Smaller squares (for example 0.5 cm) make the estimate more accurate, and the real contact area is usually smaller than the outline because the arch of the foot does not touch the floor.

Common mistakes

  • Dividing cm² by 100 to get m². The correct factor is 10 000 (and 1 000 000 for mm²).
  • Using mass in kg as the force. Pressure needs the weight in newtons: W = m g.
  • Writing p = A ÷ F. Pressure is force per area, so the force goes on top.
  • Forgetting to add up all the contact areas – four table legs, four tyres or two feet.
  • Leaving an answer in Pa when the question asks for kPa (or the other way round).

Revision questions

Try these, then check your answers below each one.

Question 1. What is the unit of pressure? (Choose from: pascal (Pa), newton (N), joule (J), newton-metre (N m).)

Answer: pascal (Pa)

Working: The pascal (Pa). 1 Pa = 1 N/m². The newton is the unit of force, the joule of energy and the newton-metre of moment.

Question 2. Convert an area of 250 cm² into m².

Answer: 0.025 m²

Working: 1 m² = 10 000 cm², so 250 ÷ 10 000 = 0.025 m².

Question 3. A full water tank presses on a floor with a pressure of 2.5 kPa. Its base has an area of 0.80 m².<br/>Calculate the force the tank exerts on the floor.

Answer: 2000 N

Working: 2.5 kPa = 2500 Pa. F = p × A = 2500 × 0.80 = 2000 N.

Related lessons

Continue in the full course

This lesson is section 11.1 (AGCPH1101) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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