Question

A 2430-N piano was hoisted 30 meters above the ground using a hydraulic lift. How strong is the force exerted on the master cylinder and how far is the master cylinder moved? The ratio of the area of the master cylinder to the area of the second cylinder is 150.

Answer 1

According to Pascal's law about confined fluid, the pressure on the master cylinder is equal to that on the second cylinder,

i.e., F_m / A_m = F_s / A_s, or, F_m = F_s x ( A_m / A_s ),

where, F and A denote force and area of cross - section of the cylinders respectively,

the subscripts m and s denotes the master and the second cylinders respectively.

Given, F_s = Weight of the piano = 2430 N, and, A_m / A_s = 150.

So, F_m = 2430 N x 150 = 3.645 x 10⁵ N.

Hence, the force exerted on the master cylinder is 3.645 x 10⁵ N.

Work done by both the cylinders must be same, according to the energy conservation priciple.

So, F_s x 30 m = F_m x d, d being the distance moved by the master cylinder.

So, d = ( F_s / F_m ) x 30 m = ( A_s / A_m ) x 30 m = ( 1 / 150 ) x 30 m = 0.2 m = 20 cm.

Hence, the master cylinder moved by 20 cm.