Consider a hydraulic lift that uses an input piston with an area of 0.5m2. An input force of 15N is exerted on this piston. If the output piston has an area of 3.5m? What is the output force?

The output force of the piston is 105 N.

Explanation:

Given;

the area of the input piston, A₁ = 0.5 m²

the input force of the piston, F₁ = 15 N

the area of the output piston, A₀ = 3.5 m²

the output force of the piston, F₀ = ?

The pressure of the  hydraulic lift is given by;

where;

P is the hydraulic pressure

F is the piston force

A is the area of the piston

Therefore,  the output force of the piston is 105 N.

Assuming the attic is ventilated to the open air the air pressure inside the house gets lower and the fan job becomes easier. It will speed up because while the pressure differential across the fan is increased, the mass of air being moved has decreased.

This can be verified by running a household vacuum cleaner in hose mode. With the hose open and air moving through it, the motor speed will be at a certain level producing a certain noise pitch . Placing your hand over the hose end will decrease the pressure in the hose, reduce the volume of air moving and you will hear an increase in motor pitch as it speeds up under lower load conditions.

The area inside the vacuum hose is akin to the inside of a well sealed house with an attic fan running.