Question

We've discussed elevators that are raised with cables, but many elevators use pistons. A pump provides fluid at very high pressure to the piston; the resulting force on the piston raises the elevator and passengers. For a typical piston elevator, the mass of the elevator and passengers is 2000 kg and the radius of the piston is a surprisingly small 4. 2 cm. The elevator begins to move upward, accelerating at 0. 80 m/s2. What is the absolute pressure in the piston?

Answer 1

$p = \frac{f}{s}$

$f = ma = 2000 \times 0.8 = 1600$

$s = \pi \: r {}^{2} = 3.14 \times 4. {2}^{2} \times 10 {}^{ - 4} = 55.42 \times 10 {}^{ - 4}$

$p = \frac{1600}{55.42 \times 10 {}^{ - 4} } = 288 \: 704 \: pascal$