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In the process of changing a flat tire, a motorist uses ahydraulic jack. She begins by applying a force of 45 N to the inputpiston, which has a radius of r1. As a result, the output plunger,which has a radius of r2, applies a force to the car. The ratior2/r1 has a value of 8.3. Ignore the height difference between theinput piston and the output plunger and determine the force thatthe output plunger applies to the car.The answer in the back of the book is 3100N but how do I getit?

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Answer:

3100.05 N

Explanation:

[tex]F_1[/tex] = Force on piston = 45 N

[tex]r_1[/tex] = Radius of piston

[tex]r_2[/tex] = Radius of plunger

[tex]\dfrac{r_2}{r_1}=8.3[/tex]

From Pascal's law we have

[tex]\dfrac{F_1}{A_1}=\dfrac{F_2}{A_2}\\\Rightarrow F_2=\dfrac{F_1A_2}{A_1}\\\Rightarrow F_2=\dfrac{F_1\pi r_2^2}{\pi r_1^2}\\\Rightarrow F_2=\dfrac{F_1r_2^2}{r_1^2}\\\Rightarrow F_2=F_1\dfrac{r_2^2}{r_1^2}\\\Rightarrow F_2=45\times 8.3^2\\\Rightarrow F_2=3100.05\ N[/tex]

The force is 3100.05 N

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