Question

A barber’s chair with a person in it weighs 2118.0 N. The output plunger of a hydraulic system begins to lift the chair when the barber’s foot applies a force of 63.0 N to the input piston. Neglect any height difference between the plunger and the piston. What is the ratio of the radius of the plunger to the radius of the piston?

Answer 1

Answer:5.8

Step-by-step explanation:

Given

weight of chair with person on it =2118 N

Barber applies a force of 63 N

Using pascal's law

we know pressure around both sides is equal

i.e. $P_{chair}=P_{piston}$

pressure=$\frac{force}{area}$

$P_{chair}$=$\frac{2118}{\pi \dot r_{plunger}^2}$

$P_{piston}$=$\frac{63}{\pi \dot r_{piston}^2}$

substituting values

$\left [\frac{r_{plunger}^2}{r_{piston}^2}\right ]$=$\frac{2118}{63}$

$\left [\frac{r_{plunger}}{r_{piston}}\right ]$=$\left [ \frac{2118}{63}\right ]^{0.5}$

$\left [\frac{r_{plunger}}{r_{piston}}\right ]$=5.798