1. 1
   A diver is exploring a shipwreck at the bottom of a harbour. She carries a flat rectangular dive plate, measuring 0.40 m by 0.25 m, which she presses against the seabed to steady herself while examining a hatch. The water above pushes down on the plate with a total force of 2000 N, spread evenly over its surface. Further out from the shore, the harbour floor slopes downward, so the water above the diver becomes progressively deeper as she swims further from the beach.

   (a)

   A diver's flat rectangular dive plate measures 0.40 m by 0.25 m and is pressed flat against the seabed by the water above it, exerting a force of 2000 N normal to the plate. What is the pressure exerted on the seabed by the plate?

   [1 mark]

   • A2000 Pa
   • B20000 Pa
   • C8000 Pa
   • D800 Pa

   (b)

   As the diver swims from the shallow part of the harbour towards the deeper part near the shipwreck, what happens to the pressure she experiences at a fixed depth below the surface, and why?

   [1 mark]

   • AIt stays the same, because pressure at a given depth does not depend on how far out to sea you are
   • BIt decreases, because the water becomes less dense further from the shore
   • CIt increases, because there is more water pushing down horizontally as she swims out
   • DIt stays the same, because pressure only depends on the diver's own weight

   (c)

   The diver descends from a point where the water above her is 6.0 m deep to a point where it is 14.0 m deep. The density of the seawater is 1030 kg/m³ and the gravitational field strength is 10 N/kg. Calculate the increase in pressure she experiences due to this change in depth.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A mechanic uses a hydraulic car lift in a garage to raise vehicles for inspection underneath. The lift consists of two connected cylinders filled with hydraulic fluid: a small piston, of area 0.02 m², which the mechanic pushes down using a foot pedal, and a much larger piston, of area 0.5 m², positioned under the car's chassis. The fluid connecting the two pistons is sealed and cannot be compressed.

   (a)

   In a garage hydraulic car lift, a mechanic pushes down on a small piston of area 0.02 m² with a force of 100 N. This pressure is transmitted through the hydraulic fluid to a larger piston of area 0.5 m², which lifts a car. What upward force does the large piston exert on the car?

   [1 mark]

   • A100 N
   • B250 N
   • C2500 N
   • D4 N

   (b)

   Which property of fluids explains why the force applied by the mechanic at the small piston can be used to lift a much heavier car at the large piston?

   [1 mark]

   • AFluids are much denser than solids, so they can support greater weights
   • BThe hydraulic fluid becomes compressed near the large piston, increasing the force there
   • CFluids flow more easily than solids, reducing the force needed to move the car
   • DPressure applied to an enclosed fluid is transmitted equally in all directions throughout the fluid

   (c)

   The mechanic replaces the small piston with one of a smaller area, 0.01 m², while keeping the same 100 N force and the same 0.5 m² large piston. Calculate the new force exerted on the car, and state what this shows about the effect of reducing the small piston's area.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A fishing buoy floats at the surface of a lake, held in place by a rope anchored to the lakebed to stop it drifting away. The buoy is a sealed hollow sphere with a weight of 45 N. When fully submerged, it displaces 6000 cm³ of lake water, which has a density of 1000 kg/m³. Take g = 10 N/kg for all calculations. A second, identical-looking buoy made from solid, dense plastic with a weight of 90 N is placed in the same lake without a rope.

   (a)

   Calculate the upthrust acting on the fully submerged buoy, and state whether the buoy would float or sink if the rope were cut, giving a reason.

   [3 marks]

   (b)

   The second, solid plastic buoy has a weight of 90 N and, when fully submerged, displaces the same volume of water as the first buoy (6000 cm³). Explain, using calculations, why this second buoy sinks to the bottom of the lake instead of floating, and describe what would need to change about the buoy for it to float instead.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A submarine can control its depth by adjusting the amount of water held in its ballast tanks. When the tanks are filled with seawater, the submarine's overall weight increases; when compressed air is pumped in to force water out, the submarine's weight decreases. A crew member also notices that the hull of the submarine is built to withstand much greater pressures near the bottom of the ocean than near the surface.

   (a)

   Explain, in terms of upthrust and weight, how adjusting the ballast tanks allows the submarine to descend, remain at a constant depth, and then ascend again. Your answer should refer to the relationship between upthrust and weight in each of these three situations.

   [6 marks]

   (b)

   The submarine's hull must be built to withstand much greater pressure when it dives to great depths near the ocean floor than when it operates near the surface. Explain why the pressure acting on the submarine's hull increases as it descends, and discuss why engineers must design the hull differently for a submarine intended for deep-ocean dives compared with one that only operates near the surface.

   [6 marks]

   Total for question 4: 12 marks

End of questions