IGCSE Physics 1.8 — Pressure Numericals (Solutions)

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IGCSE Physics 0625 · Section 1.8 · Pressure — Numerical Solutions

Pressure — Numerical Practice: Solutions

A. Pressure as Force per Unit Area

A1

Force 300 N, area 0.6 m². Find pressure.

1
p = F/A
300 ÷ 0.6
✓500 Pa
A2

Pressure 2000 Pa, area 0.05 m². Find force.

1
F = pA
2000 × 0.05
✓100 N
A3

Force 150 N, pressure 750 Pa. Find area.

1
A = F/p
150 ÷ 750
✓0.2 m²
A4

40 N over 0.02 m² vs 0.08 m². Compare pressures.

1
Face 1: p = F/A
40 ÷ 0.02 = 2000 Pa
2
Face 2: p = F/A
40 ÷ 0.08 = 500 Pa
✓The smaller face (0.02 m²) produces the greater pressure (2000 Pa vs 500 Pa)
A5

Why does a drawing pin have a sharp point?

✓A sharp point has a very small area. Since p = F/A, a small area produces a very large pressure for even a modest applied force, allowing the pin to pierce a surface easily.
A6

Why do snowshoes stop sinking?

✓Snowshoes spread the person’s weight (force) over a much larger area. Since p = F/A, a larger area for the same force produces a much smaller pressure, which is less likely to push the snow away and cause sinking.
A7

600 N over 0.0001 m². Find pressure.

1
p = F/A
600 ÷ 0.0001
✓6,000,000 Pa (6 × 10⁶ Pa)

B. Liquid Pressure

B1

Water, depth 5 m. Find pressure.

1
Δp = ρgΔh
1000 × 9.8 × 5
✓49000 Pa
B2

Water, pressure 19600 Pa. Find depth.

1
Δh = Δp/(ρg)
19600 ÷ (1000 × 9.8)
✓2 m
B3

Liquid density 800 kg/m³, depth 2 m. Find pressure.

1
Δp = ρgΔh
800 × 9.8 × 2
✓15680 Pa
B4

Compare 0.5 m depth in water vs mercury.

1
Water: Δp = ρgΔh
1000 × 9.8 × 0.5 = 4900 Pa
2
Mercury: Δp = ρgΔh
13600 × 9.8 × 0.5 = 66640 Pa
✓Mercury produces a much greater pressure (66640 Pa vs 4900 Pa) because it is far denser than water
B5

Why does pressure increase with depth?

✓At a greater depth, there is a taller column of liquid above pressing down, so its weight acts over the same area with a greater force — and since pressure is force per unit area, a greater force means a greater pressure.
B6

Pressure 500000 Pa in water. Find depth.

1
Δh = Δp/(ρg)
500000 ÷ (1000 × 9.8)
✓≈ 51.0 m
B7

Why are dams thicker at the base?

✓Water pressure increases with depth, so the water pushes hardest against the lowest part of the dam wall. Building the dam thicker at the base gives it the strength to withstand this much greater pressure where it is at its maximum.

Mastery Test — Answer Key

  1. 250 Pa (500 ÷ 2)
  2. 200 N (800 × 0.25)
  3. 0.2 m² (90 ÷ 450)
  4. A blunt knife has a wider edge (larger area), so for the same applied force, p = F/A gives a smaller pressure — meaning more force is needed to achieve the same cutting pressure as a sharp knife’s much smaller edge area.
  5. 78400 Pa (1000 × 9.8 × 8)
  6. 1 m (9800 ÷ (1000×9.8))
  7. 37240 Pa (950 × 9.8 × 4)
  8. For a constant force, increasing the area DECREASES the pressure, since p = F/A — a larger denominator with the same numerator gives a smaller result.
  9. 0.5 m²: p = 1000÷0.5 = 2000 Pa. 2 m²: p = 1000÷2 = 500 Pa. The smaller area (0.5 m²) produces the greater pressure.
  10. At greater depth, there is a taller column of liquid above pressing down, so its weight acts with a greater force over the same area — and since pressure is force per unit area, a greater force means greater pressure.

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