pressure and physics question?
In a car lift, compressed air exerts a force on a piston with a radius of 5.00 cm. This pressure is transmitted to a second piston with a radius of 15.0 cm.
a. What force must the compressed air exert to lift a car weighing 1.33 × 10^4 N?
b. What pressure is required to produce this force?
For the purposes of this calculation, please neglect the weight of the pistons.
1 Answers
In a hydraulic lift, the pressure in equals the pressure out.
P1 = P2
Pressure is force over area
P = F/A
a.
F2, the force out is 1.33e4 N
F1/A1 = F2/A2
F1 = (A1/A2)F2
A = (pi)r^2
(A1/A2) = 5^2 / 15^2 = 1/9
F1 = (1/9)F2 = (1.33e4)/9 = 1.48e3 N
b.
P1 = F1/A1 = 1.48e8 / ((pi)(0.05^2)) = 1.88e5 N/m^2 = 1.88e5 Pa
This pressure is approximately twice atmospheric pressure.
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