A mechanic raises cars with a hydraulic lift. Figure 14 models it as two connected cylinders of liquid, A and B, each with a piston, with a force F applied to piston A.
(a) Compare the pressure in cylinder A with the pressure in cylinder B. Tick one box.
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The third box. A pressure applied to a liquid in a closed space is passed on equally through the whole liquid, so the pressure is the same in both cylinders.
How the marks are earned
- Tick the third box: the pressure in A equals the pressure in B.
(b) Piston areas: A 2.0 × 10-4 m2, B 10 × 10-4 m2. F is 1000 N on A. Find the force on B.
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Pressure = force over area. For piston A:. pressure = fraction: 1000 N over 2.0 × 10-4 m2, end of fraction. = 5.0 × 106 Pa
The liquid passes the pressure on equally, so the pressure on piston B is also 5.0 × 106 Pa.. Force = pressure × area. = 5.0 × 106 Pa × 10 × 10-4 m2. = 5000 N
How the marks are earned
- One mark: pressure in A = force ÷ area with the numbers put in, 1000 ÷ 2.0 × 10-4.
- One mark: the pressure in A is 5.0 × 106 Pa (5 000 000 Pa).
- One mark: the pressure in B is the same, so force on B = pressure × area of B, with the numbers put in: 5.0 × 106 × 10 × 10-4. A wrong pressure for A carried forward correctly earns this mark.
- One mark: the force, 5000 N.
- A ratio route earns full marks: the area ratio is 10 × 10-4 ÷ 2.0 × 10-4 = 5, so the force is 5 × 1000 = 5000 N. So does equating force ÷ area for A and for B and rearranging for the force on B.
- The correct answer, 5000 N, on the answer line earns full marks.
Why it scores
Two marks: putting the numbers into pressure = force ÷ area, and the pressure worked out.
Two marks: the equal pressure used in force = pressure × area with the numbers put in, then the force. This is a force multiplier: piston B has 5 times the area, so it gets 5 times the force. The right answer alone earns all 4 marks.
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