In the hydraulic car lift as shown in the figure, the input piston on the left has a radius of 
and a negligible weight. The output plunger on the right has a radius of 
. The combined weight of the car and the plunger is 
. Suppose that the bottom surfaces of the piston and plunger are at the same level, so that 
in figure. What is the magnitude 
of the input force needed?
Text Solution
Verified by ExpertsC
The output force should have a magnitude of 
to supports the car. Initially the
piston and the plunger are at the same height, so the fluid pressure at the piston is equal to the fluid pressure at the plunger 
where 
is the area of the piston and 
is the area of the plunger.
Therefore, the magnitude of the force 
Using 
for the circular areas of the piston and plunger.
We find that,
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