Question

A barber raises his customer’s chair by applying a force of 150N to a hydraulic piston of area 0.01 $m^2$. If the chair is attached to a piston of area 0.1 $m^2$, what is the maximum weight of the customer who can be raised by using this chair? Assume the chair itself has a mass of 5 kg.

• A. 148 kg
• B. 153 kg
• C. 150 kg
• D. 100 kg

Answer 1

The correct option is A

148 kg

First, determine the force applied to the larger piston.
$F_2$ ​= ($\frac{A_2}{A_1}$) $\times$​ $F_1$ ​
$F_2$​ = ($\frac{{0.10m}^2}{{0.01m}^2}$) $\times$ (150 N) = 1500 N
If the maximum force on the chair is 1500N, now determine the maximum mass which can be lifted, therefore, the applied force on the customer must equal the force of gravity on the customer.
F = mg
m = $\frac{F}{g}$ = $\frac{1500N}{9.8\frac{m}{{sec}^2}}$​ = 153 kg
If the chair has a mass of 5 kilograms, the maximum mass of a customer in the chair must be = 153 kg – 5 kg = 148 kg.