In a hydraulic lift, if the pressure exerted on the liquid by one piston is increased by 100 N/m2 , how much additional weight can the other piston slowly lift if its cross sectional area is 25 m2

The additional weight and mass needed for lifting the other piston slowly is 2500 N and 254.92 kg, respectively.

Explanation:

By means of the Pascal's Principle, the hydraulic lift can be modelled by the following two equations:

Hydraulic Lift - Before change

Hydraulic Lift - After change

Where:

- Hydrostatic pressure, measured in pascals.

- Change in hydrostatic pressure, measured in pascals.

- Cross sectional area of the hydraulic lift, measured in square meters.

- Hydrostatic force, measured in newtons.

- Change in hydrostatic force, measured in newtons.

The additional weight is obtained after some algebraic handling and the replacing of all inputs:

Given that and , the additional weight is:

The additional mass needed for the additional weight is:

Where:

- Additional weight, measured in newtons.

- Additional mass, measured in kilograms.

- Gravitational constant, measured in meters per square second.

If and , then:

The additional weight and mass needed for lifting the other piston slowly is 2500 N and 254.92 kg, respectively.

Work = force * distance.  We must produce twice as much energy as we are lifting the weight twice as high.  But we are not increasing the force so we must increase the length of the ramp ( distance ) instead.  The new length will be twice as great as the previous length.  So 8 metres is required. 

 25 kg * 8 m = work = 100 kg * 2 m