Question

In the process of changing a flat tire, a motorist uses a hydraulic jack. She begins by applying a force of 58 N to the input piston, which has a radius r1. As a result, the output plunger, which has a radius r2, applies a force to the car. The ratio r2/r1 has a value of 8.2. Ignore the height difference between the input piston and output plunger and determine the force that the output plunger applies to the car.

Answer 1

The correct answer is "3899.92 N".

Step-by-step explanation:

The given values are:

Force,

`F_(app)=58 N`

Ratio,

`(R_2)/(R_1)=8.2`

As we know,

Area,
`A=\pi r^2`

or,

⇒
`(F_2)/(F_1) =(A_2)/(A_1)`

On substituting the value of "A", we get

⇒
`(F_2)/(F_1) =(\pi r_2^2)/(\pi r_1^2)`

⇒
`(F_2)/(F_1) =(r_2^2)/(r_1^2)`

On applying cross-multiplication, we get

⇒
`F_2=F_1* ((r_2)/(r_1) )^2`

On substituting the given values, we get

⇒
`=58* (8.2)^2`

⇒
`=58* 67.2`

⇒
`=3899.92 \ N`