5.10 Pressure in liquids and upthrust
9 exam questions worth 24 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
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What happens to the pressure in a liquid as the depth increases?
Choose one answer.
Correct Not quite: the answer is It increases
Mark scheme
C: It increases
Model answer
It increases (C).
Calculate the pressure due to the water at the bottom of a tank of depth 2.5 m. The density of water is 1000 kg/m³ and g = 9.8 N/kg.
Mark scheme
p = h ρ g (1); 2.5 × 1000 × 9.8 (1); 24 500 Pa (1)
Model answer
p = h ρ g = 2.5 × 1000 × 9.8 = 24 500 Pa.
The pressure due to a liquid at a depth of 4.0 m is 36 000 Pa. Calculate the density of the liquid. (g = 9.8 N/kg)
Mark scheme
ρ = p ÷ (h g) (1); 36 000 ÷ (4.0 × 9.8) (1); 920 kg/m³ (1)
Model answer
ρ = p / (h g) = 36 000 / (4.0 × 9.8) = 920 kg/m³ (to 2 s.f.).
Explain why the pressure in a liquid is greater at the bottom of a container than near the surface.
Mark scheme
there is more liquid above the point / a greater weight of liquid above (1); so the pressure is greater (1)
Model answer
There is a greater weight of liquid above the bottom, so the pressure there is greater.
Explain why the water jets from the lowest hole of a container travel further than those from the highest hole.
Mark scheme
the pressure is greater at a greater depth (1); so the water is pushed out with a higher speed (1)
Model answer
The pressure is greater at the lower hole because it is deeper, so the water is pushed out at a higher speed and travels further.
Explain how the pressure of a liquid produces an upthrust on a submerged object.
Mark scheme
the pressure increases with depth (1); the bottom of the object is deeper so the pressure on it is greater than on the top (1); so the upward force on the bottom is greater than the downward force on the top, giving an upward resultant force (1)
Model answer
Pressure increases with depth, so the pressure on the bottom of the object is greater than on its top. This makes the upward force on the bottom greater than the downward force on the top, so there is a resultant upward force, the upthrust.
A block of volume 0.0030 m³ is fully submerged in water of density 1000 kg/m³. Calculate the upthrust on the block. (g = 9.8 N/kg)
Mark scheme
mass of water displaced = 1000 × 0.0030 = 3.0 kg (1); weight = 3.0 × 9.8 (1); 29.4 N (1)
Model answer
Mass of water displaced = 1000 × 0.0030 = 3.0 kg. Upthrust = weight of this water = 3.0 × 9.8 = 29.4 N.
A boat floats on the sea. State the size of the upthrust compared with the weight of the boat, and explain what happens if cargo is added to the boat.
Mark scheme
upthrust equals the weight of the boat (1); with more cargo the weight is greater, so the boat sinks lower (1); and displaces more water so the upthrust increases until it equals the new weight (1)
Model answer
The upthrust equals the weight of the boat. If cargo is added, the weight increases, so the boat sinks lower and displaces more water, until the upthrust is equal to the new weight.
A steel ball sinks in water but a steel ship floats. Explain the difference in terms of forces.
Mark scheme
the ball has a high density / its weight is greater than the upthrust (1); the resultant force is downwards so it sinks (1); the ship is hollow / contains a lot of air so displaces a large volume of water (1); the upthrust equals the weight of the ship so it floats (1)
Model answer
The steel ball displaces a small volume of water, so the upthrust is less than its weight and it sinks. The ship has a huge volume that is mostly air, so it displaces a lot of water. The upthrust then equals the ship's weight, so it floats.
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