Answers · Pressure

Force and area — answer key

Check meaning, not exact wording. These are teaching points, not official Cambridge marks.

1. PRQ1 · Practice

Model answer. Pressure is the force per unit area: the force acting on each square metre of a surface, p = F / A. Its unit is the pascal, 1 Pa = 1 N/m². Force × area would make a larger area give a larger pressure, the wrong way round. A volume or a mass is not part of a pressure.

A full answer includes

I chose force per unit area.
I did not choose force × area.

Also accept

force per unit area

Watch for

“Force × area.” — Multiplying by the area would make a larger area give a larger pressure. Pressure is force divided by area: a larger area gives a smaller pressure.
“Force per unit volume.” — A pressure acts on a surface, so the force is shared over an area in m², not a volume in m³.
“Mass per unit area.” — A pressure comes from a force in newtons, not a mass in kilograms. Its unit is N/m², not kg/m².

2. PRQ2 · Practice

Model answer. Pressure = force ÷ area = 50 N ÷ 2.0 m² = 25 Pa. Each square metre carries 25 N.

Checked automatically

Pressure: 25 Pa (within ±0.5 Pa)
- Common wrong answer 100 : Divide the force by the area; do not multiply.
- Common wrong answer 0.04 : Divide the force by the area, not the area by the force.

A full answer includes

Method: I divided 50 N by 2.0 m².
Answer: I wrote 25 Pa (or 25 N/m²).
I did not multiply the force by the area.

Also accept

25 Pa

Watch for

“p = 50 × 2.0 = 100 Pa.” — Pressure is force divided by area, not multiplied.

3. PRQ3 · Practice

Options as numbered on the pupil sheet: 1 — 0.0035 m²; 2 — 2.0 m²; 3 — 7.5 m²; 4 — 0.075 m²; 5 — 0.0002 m².

Model answer. A square metre is 100 cm by 100 cm, so it holds 100 × 100 = 10 000 cm². Divide each area in cm² by 10 000: 20 000 cm² = 2.0 m², 750 cm² = 0.075 m², 35 cm² = 0.0035 m² and 2 cm² = 0.0002 m². 7.5 m² is what you get if you wrongly divide 750 by 100.

A full answer includes

I matched 20 000 cm² to 2.0 m².
I matched 750 cm² to 0.075 m².
I matched 35 cm² to 0.0035 m².
I matched 2 cm² to 0.0002 m².
I did not use 7.5 m², which comes from dividing by 100.

Also accept

20 000 cm² – 2.0 m²; 750 cm² – 0.075 m²; 35 cm² – 0.0035 m²; 2 cm² – 0.0002 m²

Watch for

“To change cm² into m², divide by 100.” — There are 100 cm in a metre, but 100 × 100 = 10 000 cm² in a square metre.

4. PRQ4 · Practice

Model answer. The force on the feet is the weight, which is now 2 times as large. The area is 3 times as large. Pressure = force ÷ area, so the new pressure is 2 ÷ 3 = two-thirds of the old one. The larger feet more than make up for the extra weight.

A full answer includes

I chose two-thirds as large.
I did not multiply the two changes together.

Also accept

two-thirds as large

Watch for

“1.5 times as large.” — You divided the area change by the force change. Pressure = force ÷ area, so the change is 2 ÷ 3.
“Six times as large.” — You multiplied the two changes. A larger area makes the pressure smaller, so divide by 3.
“The same as before.” — The force doubles and the area triples. These do not cancel: work out 2 ÷ 3.

5. PRQ5 · Practice

Model answer. Area = 15 cm × 8.0 cm = 120 cm². In m²: 120 ÷ 10 000 = 0.012 m². Pressure = 30 N ÷ 0.012 m² = 2500 Pa.

Checked automatically

Pressure: 2500 Pa (within ±50 Pa)
- Common wrong answer 0.25 : That uses the area in cm². Change 120 cm² into m² first.
- Common wrong answer 25 : To change cm² into m², divide by 10 000, not by 100.

A full answer includes

Method: I multiplied 15 cm by 8.0 cm to get 120 cm².
Method: I changed 120 cm² into 0.012 m².
Method: I divided 30 N by 0.012 m².
Answer: I wrote 2500 Pa.
I did not divide by the area in cm².

Also accept

2500 Pa

Watch for

“p = 30 ÷ 120 = 0.25 Pa.” — That uses the area in cm². Change it into m² first.

6. PRQ6 · Practice

Model answer. Rearrange p = F / A for the force: F = pA. The weight is shared by four feet, so the total area is 4 × 0.10 m² = 0.40 m². F = 125 000 Pa × 0.40 m² = 50 000 N. Each foot carries 125 000 Pa × 0.10 m² = 12 500 N, and 4 × 12 500 N is the same 50 000 N.

Checked automatically

Weight: 50000 N (within ±500 N)
- Common wrong answer 12500 : That is the force on one foot. Use the area of all four feet.
- Common wrong answer 1250000 : Force = pressure × area; multiply, do not divide.

A full answer includes

Method: I rearranged p = F / A to F = pA.
Method: I worked out 125 000 Pa × 0.40 m², the area of all four feet (or 4 × 12 500 N).
Answer: I wrote 50 000 N.
I did not use the area of one foot only.

Also accept

50 000 N

Watch for

“F = 125 000 × 0.10 = 12 500 N.” — That is the force on one foot. The elephant’s weight is shared by all four.
“F = 125 000 ÷ 0.10 = 1 250 000 N.” — Force = pressure × area. Dividing gives the wrong quantity.

7. PRQ7 · Practice

Model answer. The force on the mat is the runner’s weight, 720 N. Rearrange p = F / A for the area: A = F / p = 720 N ÷ 40 000 Pa = 0.018 m², which is 180 cm².

Checked automatically

Area: 0.018 m² (within ±0.0005 m²)
- Common wrong answer 55.6 : Area = force ÷ pressure: put the force on top.

A full answer includes

Method: I rearranged p = F / A to A = F / p.
Method: I divided 720 N by 40 000 Pa.
Answer: I wrote 0.018 m².
I did not divide the pressure by the force.

Also accept

0.018 m²

Watch for

“A = 40 000 ÷ 720 = 55.6 m².” — Area = force ÷ pressure, with the force on top. 55.6 m² is about the floor of a classroom, far too large for a foot.

8. PRQ8 · Practice

Model answer. The force on the floor is the person’s weight, the same in both pairs of shoes. The heels put that weight on a much smaller area. Pressure = force ÷ area, so the pressure under the heels is much larger, and the vinyl gives way.

A full answer includes

I chose: the same force acts on a smaller area, so the pressure is larger.
I did not choose a larger force.

Also accept

the same force on a smaller area, so a larger pressure

Watch for

“The same force acts on a smaller area, so the pressure is smaller.” — A smaller area makes the pressure larger, not smaller: the same force is shared over fewer square metres.
“A larger force acts on the floor, so the pressure is larger.” — The force on the floor is the person’s weight, which is the same in both pairs of shoes.
“A harder material touches the floor, so the pressure is larger.” — How hard the heel is changes neither the force nor the area, and pressure = force ÷ area. Flat soles can be just as hard.

9. PRQ9 · Practice

Options as numbered on the pupil sheet: 1 — A small area makes the pressure large.; 2 — The area does not change the pressure.; 3 — A large area makes the pressure small..

Model answer. Skis, caterpillar tracks and a board on mud must stay on top of a soft surface. They spread a weight over a large area, so the pressure is small and they do not sink into the snow or the mud. An ice-skate blade must grip the ice, and a tent peg must go into the ground. They put a force on a tiny area, so the pressure is large. The first three work like snowshoes; the last two work like a drawing pin.

A full answer includes

I matched the skis to: a large area makes the pressure small.
I matched the caterpillar tracks to: a large area makes the pressure small.
I matched the board on the mud to: a large area makes the pressure small.
I matched the blade of the ice skate to: a small area makes the pressure large.
I matched the tip of the tent peg to: a small area makes the pressure large.
I did not use: the area does not change the pressure.

Also accept

skis, tracks, board – a large area makes the pressure small; skate blade, tent peg – a small area makes the pressure large

Watch for

“The area does not change the pressure.” — Pressure = force ÷ area, so the same force on a larger area gives a smaller pressure, and on a smaller area a larger one.
“A skate blade is narrow only to make it light.” — Its edge touches the ice over a tiny area, so the skater’s weight gives a large pressure on the ice, and the blade grips.

10. PRQ10 · Practice

Model answer. (a) The force is the same at both ends, and pressure = force ÷ area. The point’s area is 32 mm² ÷ 0.40 mm² = 80 times smaller, so the pressure on the finger is 80 times larger. The areas do not need changing into m², because only their ratio matters. (b) The pressure on her finger doubles: twice the force on the same area gives twice the pressure.

A full answer includes

(a) Method: I divided the area at the thumb, 32 mm², by the area at the point, 0.40 mm².
(a) Answer: I wrote 80 times.
(a) I did not divide 0.40 by 32.
(b) I wrote that the pressure on her finger doubles.
(b) I said the force doubles on the same area.

Also accept

(a) 80 times (b) it doubles

Watch for

“The point pushes harder on the finger than the flat end pushes on the thumb.” — The pencil is still, so the two forces are equal. Only the areas are different.
“The pressure on the finger is 0.40 ÷ 32 = 0.0125 times the pressure on the thumb.” — The smaller area gets the larger pressure, so divide the larger area by the smaller one.

11. PRQ11 · Practice

Options as numbered on the pupil sheet: 1 — A car of weight 10 000 N on the same wide sand tyres, 0.25 m² in all; 2 — A beach buggy of weight 5000 N on wide sand tyres, 0.25 m² in all; 3 — A motorbike of weight 3000 N on its two tyres, 0.015 m² in all; 4 — The same car on its ordinary tyres, 0.080 m² in all.

Model answer. Pressure = force ÷ area: buggy 5000 N ÷ 0.25 m² = 20 000 Pa; car on wide tyres 10 000 N ÷ 0.25 m² = 40 000 Pa; car on ordinary tyres 10 000 N ÷ 0.080 m² = 125 000 Pa; motorbike 3000 N ÷ 0.015 m² = 200 000 Pa. The lightest vehicle gives the largest pressure, because its tyres touch the sand over such a small area.

A full answer includes

I put the buggy on wide sand tyres first (20 000 Pa).
I put the car on wide sand tyres second (40 000 Pa).
I put the car on its ordinary tyres third (125 000 Pa).
I put the motorbike last (200 000 Pa).
I did not put the motorbike first because it is the lightest.

Also accept

buggy on wide tyres, car on wide tyres, car on ordinary tyres, motorbike

Watch for

“The lightest vehicle always presses least.” — The 3000 N motorbike presses hardest of all, because its two tyres touch the sand over only 0.015 m².

12. PRQ12 · Practice

Model answer. The same weight gives the greatest pressure on the smallest area, so the block must stand on its smallest face, 0.15 m by 0.10 m. Its area is 0.15 m × 0.10 m = 0.015 m². Pressure = 45 N ÷ 0.015 m² = 3000 Pa. On its largest face, 0.40 m × 0.15 m = 0.060 m², the same block gives only 750 Pa.

Checked automatically

Greatest pressure: 3000 Pa (within ±50 Pa)
- Common wrong answer 750 : That is the pressure on the largest face, 0.40 m × 0.15 m. The greatest pressure is on the smallest face.
- Common wrong answer 1125 : That is the pressure on the face 0.40 m × 0.10 m. Use the smallest face, 0.15 m × 0.10 m.

A full answer includes

Method: I chose the smallest face, 0.15 m × 0.10 m.
Method: I worked out its area, 0.015 m².
Method: I divided 45 N by 0.015 m².
Answer: I wrote 3000 Pa.
I did not use the largest face, 0.40 m × 0.15 m.

Also accept

3000 Pa

Watch for

“Use the largest face: 45 ÷ 0.060 = 750 Pa.” — The largest face gives the smallest pressure. The greatest pressure comes from the smallest face.

13. PRT1 · Apply

Model answer. (a) A = F / p = 650 N ÷ 10 000 Pa = 0.065 m². On any smaller area, the pressure is more than 10 000 Pa. (b) No. 0.040 m² is smaller than 0.065 m², so the pressure is more than the ice can carry: 650 N ÷ 0.040 m² = 16 250 Pa. The ice cracks. (c) Lying flat, the force on the ice is still their weight, 650 N, but it is spread over the much larger area of the body. Pressure = force ÷ area, so the pressure is much smaller and can be below 10 000 Pa.

A full answer includes

(a) Method: I rearranged p = F / A to A = F / p.
(a) Method: I divided 650 N by 10 000 Pa.
(a) Answer: I wrote 0.065 m².
(b) I wrote that the ice will not hold them: it cracks.
(b) I said 0.040 m² is smaller than 0.065 m² (or that 650 N ÷ 0.040 m² = 16 250 Pa, more than 10 000 Pa).
(c) I said the force on the ice, their weight, stays the same.
(c) I said lying flat spreads it over a larger area.
(c) I said a larger area gives a smaller pressure.
I did not write that lying down makes the person lighter.

Also accept

(a) 0.065 m² (b) no: 0.040 m² is smaller than 0.065 m² (c) the same force on a larger area gives a smaller pressure

Watch for

“Lying down makes you lighter on the ice.” — Your weight is the same; only the area it acts on changes.
“The soles are smaller than 0.065 m², so the ice holds.” — A smaller area gives a larger pressure. Below the smallest safe area, the pressure is too large.