Question

An external pressure applied to an enclosed fluid in a hydraulic lift. Piston 1 has a radius that is 1/200 the radius of piston 2 (r1 = r2/200). If the bottom of both pistons start from the same vertical height, how much force needs to by applied to the first piston in order to begin lifting a weight of 20,000 N positioned atop the second piston?

Answer 1

Answer:

0.5 N

Explanation:

$r_{1}$ = radius of piston 1

$r_{2}$ = radius of piston 2

Given that :

$r_{2} = 200 r_{1}$

$F_{1}$ = Force applied on piston 1

$F_{2}$ = Force applied on piston 2 = Weight being lifted = 20000 N

Using pascal's law

$\frac{F_{1}}{\pi r_{1}^{2} } = \frac{F_{2}}{\pi r_{2}^{2} } \\\frac{F_{1}}{r_{1}^{2} } = \frac{20000}{(200)^{2}r_{1}^{2} } \\\\F_{1}= \frac{20000}{(200)^{2}} } \\F_{1}= 0.5 N$