A hydraulic lift is used to raise a `1500 kg` automobile. The radius of the shaft of the lift is `8.00 cm` and the radius of the compressor's piston is `1.00 cm` . How much force must be applied  to...

A hydraulic lift is used to raise a `1500 kg` automobile. The radius of the shaft of the lift is `8.00 cm` and the radius of the compressor's piston is `1.00 cm` . How much force must be applied  to the piston to raise the automobile?

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The pressure applied to an enclosed liquid is transmitted undiminished to every point in the fluid and to the walls of the container. Hence we can equate the pressure produced by the force applied to the piston to the pressure due to the weight of the automobile and solve for `F` .

Express the pressure the weight of the automobile exerts on the shaft of the lift.

`P_(a u t o)=w_(a u t o)/A_(s h a f t)`

Express the pressure the force applied to the piston produces.

`P=F/A_(p i s t o n)`

We want to know how much force is need to make `P=P_( a u t o)` . Therefore,

`P=P_(a u t o)`

`F/A_(p i s t o n)=w_(a u t o)/A_(s h a f t)`

`F=w_(a u t o)*(A_(p i s t o n)/A_(s h a f t))`

`F=m_(a u t o)g*(A_(p i s t o n)/A_(sh a f t))`

`F=(1500 kg)*(9.81 m/s^2)*((1.00 cm)/(8.00 cm))^2`

`F=230 N`

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