Answers · Pressure

Pressure — final check key

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

1. PRK1 · Final check

Model answer. (a) Pressure is the force per unit area, p = F / A. (b) A = F / p = 900 N ÷ 60 000 Pa = 0.015 m². In cm²: 0.015 × 10 000 = 150 cm². (c) The smallest safe area gets larger. The heavier person makes the force on the lawn larger. On the same area, that would give a pressure above 60 000 Pa, so the legs need a larger area to keep the pressure low enough.

A full answer includes

(a) I wrote that pressure is the force per unit area.
(a) I did not write force × area.
(b) Method: I divided 900 N by 60 000 Pa to get 0.015 m².
(b) Method: I multiplied 0.015 m² by 10 000 to change it into cm².
(b) Answer: I wrote 150 cm².
(b) I did not multiply by 100, which gives 1.5 cm².
(c) I wrote that the smallest safe area gets larger.
(c) I said the force on the lawn is larger.
(c) I said that on the same area, a larger force would give a pressure above 60 000 Pa.

Also accept

(a) force per unit area (b) 150 cm² (c) larger: a larger force needs a larger area to keep the pressure at 60 000 Pa or less

Watch for

“0.015 m² = 1.5 cm².” — There are 10 000 cm² in 1 m², so multiply by 10 000: 150 cm².
“The smallest safe area does not depend on the weight.” — The area must be at least force ÷ safe pressure, so a larger force needs a larger area.

2. PRK2 · Final check

Model answer. (a) The reading decreases. Depth is measured down from the surface. At first the sensor is 5.2 m − 1.2 m = 4.0 m below the surface; afterwards it is 3.2 m − 1.2 m = 2.0 m below it. With less juice above it, the pressure on it is smaller. (b) ∆p = ρg∆h = 1050 kg/m³ × 9.8 N/kg × 5.2 m = 53 508 Pa, about 53 500 Pa. (c) The syrup tank. For the syrup, ∆p = 1300 kg/m³ × 9.8 N/kg × 4.4 m = 56 056 Pa, more than the juice’s 53 508 Pa. The syrup is less deep, but it is so much denser that its pressure at the bottom is greater.

A full answer includes

(a) I wrote that the reading decreases.
(a) I said the sensor is now less deep below the surface: 2.0 m instead of 4.0 m.
(a) I said a smaller depth gives a smaller pressure.
(a) I did not write that the reading stays the same because the sensor did not move.
(b) Method: I multiplied 1050 kg/m³ × 9.8 N/kg × 5.2 m.
(b) Answer: I wrote 53 508 Pa (or 53 500 Pa, or 54 000 Pa).
(b) I did not use 4.0 m, the depth of the sensor.
(c) Method: I worked out 1300 kg/m³ × 9.8 N/kg × 4.4 m = 56 056 Pa (or compared density × depth).
(c) Answer: I wrote that the syrup tank has the greater pressure.
(c) I did not choose the juice tank only because it is deeper.

Also accept

(a) it decreases: the sensor is 2.0 m, not 4.0 m, below the surface (b) 53 508 Pa, about 53 500 Pa (c) the syrup tank: 56 056 Pa is more than 53 508 Pa

Watch for

“The sensor has not moved, so its reading stays the same.” — Depth is measured down from the surface. As the level falls, the sensor has less juice above it, so its reading decreases.
“The juice tank is deeper, so its pressure at the bottom is greater.” — Density counts as well as depth. 1300 × 4.4 is more than 1050 × 5.2, so the syrup tank’s pressure is greater.