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

0.5 N

Step-by-step 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

`(F_(1))/(\pi r_(1)^(2) ) = (F_(2))/(\pi r_(2)^(2) ) \\(F_(1))/(r_(1)^(2) ) = (20000)/((200)^(2)r_(1)^(2) ) \\\\F_(1)= (20000)/((200)^(2)) } \\F_(1)= 0.5 N`