Question

A hydraulic system for a dentist's chair is designed to be able to lift 3,112 newtons. The surface area over which this force is applied is 707 cm 2 . What force must be applied to the activator end of the system if the button has a surface area of 3.14 cm 2 ?
A:700,700 N
B:1.41 N
C:0.0724 N
D:13.8 N

Answer 1

D.13.8 N
hope i helped

Answer 2

Answer:

D. 13.8 N

Explanation:

This problem can be solved by applying Pascal's principle, which states that the pressure is transmitted equally through all of the parts of the fluid inside the hydraulic system. So, the pressure on the two ends of the system is equal:

$p_1 = p_2\\\frac{F_1}{A_1}=\frac{F_2}{A_2}$

where:

$F_1 = 3,112 N$ is the force on the first piston

$A=707 cm^2$ is the surface area of the first piston

$F_2 = ?$ is the force to be applied on the activator end

$A_2 = 3.14 cm^2$ is the surface area of the activator end

Re-arranging the equation, we get:

$F_2 = A_2 \frac{F_1}{A_1}=(3.14 cm^2 )\frac{3,112 N}{707 cm^2}=13.8 N$