A hydraulic lift in a garage has two pistons: a small one of cross-sectional are

Question

A hydraulic lift in a garage has two pistons: a small one of cross-sectional area 4.40 cm2 and a large one of cross-sectional area 230 cm2 . Part A If this lift is designed to raise a 3400-kg car, what minimum force must be applied to the small piston? F=__N Part B If the force is applied through compressed air, what must be the minimum air pressure applied to the small piston? p=__Pa
A hydraulic lift in a garage has two pistons: a small one of cross-sectional area 4.40 cm2 and a large one of cross-sectional area 230 cm2 . Part A If this lift is designed to raise a 3400-kg car, what minimum force must be applied to the small piston? F=__N Part B If the force is applied through compressed air, what must be the minimum air pressure applied to the small piston? p=__Pa
A hydraulic lift in a garage has two pistons: a small one of cross-sectional area 4.40 cm2 and a large one of cross-sectional area 230 cm2 . A hydraulic lift in a garage has two pistons: a small one of cross-sectional area 4.40 cm2 and a large one of cross-sectional area 230 cm2 . A hydraulic lift in a garage has two pistons: a small one of cross-sectional area 4.40 cm2 and a large one of cross-sectional area 230 cm2 . Part A If this lift is designed to raise a 3400-kg car, what minimum force must be applied to the small piston? F=__N Part B If the force is applied through compressed air, what must be the minimum air pressure applied to the small piston? p=__Pa
Part A If this lift is designed to raise a 3400-kg car, what minimum force must be applied to the small piston? F=__N Part B If the force is applied through compressed air, what must be the minimum air pressure applied to the small piston? p=__Pa
Part A If this lift is designed to raise a 3400-kg car, what minimum force must be applied to the small piston? F=__N Part B If the force is applied through compressed air, what must be the minimum air pressure applied to the small piston? p=__Pa
Part B If the force is applied through compressed air, what must be the minimum air pressure applied to the small piston? p=__Pa

Explanation / Answer

Since the system operates at constant pressure, the force on each piston is proportional to its area. In this case, one piston has 230/4.40 = 52.27times the area of the other. That means 1 Newton of force on the small piston is multiplied into 52.27Newtons of force on the large piston.

First we must find the weight of the car:
W = m*g
where W is weight, m is mass, and g is gravity.
W = (3,400 kg) * (9.81 m/s^2)
W = 33354 N

So the car pushes down with 33354 N of force. Presumably it is on the large piston. The applied force with which we must push on the small piston to exactly balance the car is:
Fapplied = (33354 N) / 52.27
Fapplied = 638.10 N

If the force is applied via gas pressure (or liquid pressure), we can convert this force into a pressure using the definition of pressure:
P = F / A
where P is pressure, F is force, and A is area.
P = (638.10 N) / (4.40 cm^2)
P = (638.10 N) / (0.00044 m^2)
P = 1450227 N/m^2
P = 1450227 Pa

The pressure on the small piston (which ends up being the same pressure on the large piston) must be 1450227 Pascals,

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