Question

A 11 547,83-N car is raised using a hydraulic lift, which

consists of a U-tube with arms of unequal areas, filled with
incompressible oil and capped at both ends with tight-fitting
pistons. The wider arm of the U-tube has a radius of 5 cm and the
narrower arm has a radius of 19,56 cm. The car rests on the piston
on the wider arm of the U-tube. The pistons are initially at the
same level. What is the initial force that must be applied to the
smaller piston in order to start lifting the car? (For purposes of
this problem, you can neglect the weight of the pistons.) Answer in
two decimal places.

Answer 1

75457.54816 N

Step-by-step explanation:

`F_1` = Initial force

`F_2` = Weight of car = 11547.83 N

`r_1` = Smaller radius = 5 cm

`r_2` = Larger radius = 19.56 cm

From Pascal's law we have

`(F_1)/(A_1)=(F_2)/(A_2)\\\Rightarrow F_1=F_2(A_1)/(A_2)\\\Rightarrow F_1=11547.83(\pi r_1^2)/(\pi r_2^2)\\\Rightarrow F_1=11547.83(5^2)/(19.56^2)\\\Rightarrow F_1=754.57548\ N`

The force is 754.57548 N