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

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=
`(force)/(area)`

`P_(chair)`=
`(2118)/(\pi \dot r_(plunger)^2)`

`P_(piston)`=
`(63)/(\pi \dot r_(piston)^2)`

substituting values

`\left [(r_(plunger)^2)/(r_(piston)^2)\right ]`=
`(2118)/(63)`

`\left [(r_(plunger))/(r_(piston))\right ]`=
`\left [ (2118)/(63)\right ]^(0.5)`

`\left [(r_(plunger))/(r_(piston))\right ]`=5.798