A hydraulic lift is used to jack a 870 kg car 12 cm off the floor. The diameter of the output piston is 18 cm,

Question

A hydraulic lift is used to jack a 870 kg car 12 cm off the floor. The diameter of the output piston is 18 cm, and the input force is 250 N.

(a) What is the area of the input piston?

m2

(b) What is the work done in lifting the car 12 cm?

J

(c) If the input piston moves 13 cm in each stroke, how high does the car move up for each stroke?

m

(d) How many strokes are required to jack the car up 12 cm?

(e) Calculate the combined work input of all of the strokes.

J

Answer 1

(a)

Pressure in equals pressure out:  P1 = P2

(P = F / A)

F1 / A1 = F2 / A2  -->  A1 = (F1 * A2) / F2 = ...

(F2 = m*g)

(b)

Work = force out × distance moved:

W = F2 * y = ...

(y = 12cm = 0.12m)

(c)

Volume moved by piston 1 equals volume moved by piston 2:  V1 = V2

(V = A * h)

A1 * h1 = A2 * h2  -->  h2 = (A1 * h1) / A2 = ...

(h1 = 13cm = 0.13m)

(d)

Number of strokes required equals total height divided by incremental height:

n = y / h2 = ...

(e)

Total work (for all strokes) = force in × distance moved × # of strokes:

W = F*d*n = F1 * h1 * n = ...