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

Answer:

The correct answer is "3899.92 N".

Explanation:

The given values are:

Force,

$F_{app}=58 N$

Ratio,

$\frac{R_2}{R_1}=8.2$

As we know,

Area, $A=\pi r^2$

or,

⇒  $\frac{F_2}{F_1} =\frac{A_2}{A_1}$

On substituting the value of "A", we get

⇒  $\frac{F_2}{F_1} =\frac{\pi r_2^2}{\pi r_1^2}$

⇒  $\frac{F_2}{F_1} =\frac{r_2^2}{r_1^2}$

On applying cross-multiplication, we get

⇒  $F_2=F_1\times (\frac{r_2}{r_1} )^2$

On substituting the given values, we get

⇒       $=58\times (8.2)^2$

⇒       $=58\times 67.2$

⇒       $=3899.92 \ N$