A hydraulic press consists of two cylinders of cross-sectional radii r\(_1\) m and 4r\(_1\) m, respectively. What force should be exerted on the smaller piston for a force of 3200 N to be experienced on the larger piston?
A
200N
B
1600N
C
800N
D
400N
Verified Correct Answer: A.
Physical Principles & Numerical Solution
In a hydraulic press, pressure is the same on both pistons:
\(\frac{F_1}{A_1} = \frac{F_2}{A_2}\)
Area is proportional to r\(^2\), so
F\(_1\) = F\(_2\) x \((\frac{r_1}{4r_1})^2\)
F\(_1\) = 3200 x \(\frac{1}{16}\) ( r\(_1\) cancels out)
F\(_1\) = 200N
Source: Myschool Past Questions Archive (Record #78273)