The questions are on the fluid mechanics test. Take it under real conditions before reading the mark scheme.
Quick answer: Fluids obey a few linked rules: density is mass per volume, pressure rises with depth as P = P₀ + ρgh, buoyant force equals the weight of fluid displaced, continuity says Av is constant in a pipe, and Bernoulli shows that faster flow means lower pressure. This mark scheme gives the model answers and the marks for the 8 questions of the AP Physics 1 test on fluid mechanics, from pressure on a surface to boat in the sea, with the equivalent answers to accept.
Award marks as shown for method, substitution and final answer. In explanation questions, accept any wording that states the correct physical law and links it to the observation. Do not penalise a unit slip twice.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 8
Question 1 Pressure on a surface (2 marks)
(a) P = F/A = 600 / 0.020 = 3.0 × 10⁴ Pa.
(b) The area doubles, so the pressure is halved to 1.5 × 10⁴ Pa.
Marking: 1 mark for the substitution and answer in (a); 1 mark for halving in (b).
Question 2 Pressure at 8 m (3 marks)
ρgh = 1000 × 9.81 × 8.0 = 7.85 × 10⁴ Pa. P = 1.01 × 10⁵ + 0.785 × 10⁵ = 1.79 × 10⁵ Pa.
Marking: 1 mark for P = P₀ + ρgh; 1 mark for ρgh; 1 mark for the final answer with unit.
Question 3 Thick dam walls (2 marks)
Pressure increases linearly with depth (P = P₀ + ρgh), so the horizontal force of the water is largest at the bottom. The wall needs more strength there, hence it is thicker at the base. Pressure grows with depth.
Marking: 1 mark for pressure increasing with depth; 1 mark for linking this to greater force at the base.
Question 4 Floating cube (3 marks)
(a) m = 700 × 1.0 × 10⁻³ = 0.70 kg; W = 0.70 × 9.81 = 6.9 N.
(b) Floating: B = W, so ρw g A h = W: 1000 × 9.81 × 0.010 × h = 6.867, giving h = 0.070 m.
Marking: (a) 1 mark; (b) 1 mark for setting B = W, 1 mark for the answer.
Question 5 River narrowing (2 marks)
The flow rate must stay the same, Av = constant. Half the cross-section means the water must move twice as fast, so the speed becomes 1.0 m/s.
Marking: 1 mark for continuity; 1 mark for doubling.
Question 6 Water pipe rising (3 marks)
The diameter is constant, so the speed is unchanged. P₂ = P₁ − ρgΔy = 2.50 × 10⁵ − 1000 × 9.81 × 4.0 = 2.50 × 10⁵ − 0.392 × 10⁵ = 2.1 × 10⁵ Pa.
Marking: 1 mark for constant speed; 1 mark for the ρgΔy term; 1 mark for the final answer.
Question 7 Lift in wind (2 marks)
Fast air moving over the outside has lower pressure (P + ½ρv² is constant). The air inside is nearly still and at higher pressure, so a net upward force acts on the roof. Faster air gives lower pressure.
Marking: 1 mark for lower pressure where speed is higher; 1 mark for the pressure difference giving an upward force.
Question 8 Boat in the sea (3 marks)
The weight of the boat does not change, so the buoyant force is the same. Seawater is denser than river water, so a smaller volume of water has to be displaced to give the same force. The boat floats higher.
Marking: 1 mark for buoyant force equal to weight; 1 mark for the higher density; 1 mark for the conclusion.
