Question

A hydraulic lift is to be used to lift a 2000-kg weight by putting a weight of 25 kg on a piston with a diameter of 10 cm. Determine the diameter of the piston on which the weight is to be placed.

Answer 1

Diameter=28,4849

Explanation:

Remember that the formula for pistons is oftena simple rule of three, the input and output force is equal to the division of the force by the area of the application of the force:

`(25)/(78,5)= (2000)/(x)\\ x=(2000*25)/(78,5) \\x=636,94cm^2`

Now that is the area of the circle, we just solve the formula of the circle to calculate the radius:

`a=\pi r^2\\r=\sqrt{(636,94)/(3,14) } \\r=14,24 cm`

Now remember that the radius is half the diameter so we just have to multiply the radius by 2:

14,24*2=28,4849

So the diameter has to be 28,4849

Answer 2

88 centimeters is the diameter of the cilinder

Explanation:

The pressure on both ends of the lift must be the same. Assuming the piston is cilindrical, its area will be A=π*r² where r is half the diameter

Since pressure P=F/A And P1=P2

F1=2000kg.g

A1=π*r²

F2=25kg.g

A2=π*0.05²

2000/(π*r²)=25/(π*0.05²)

and we solve for A1

r²=2000*0.05²/25

`r=\sqrt{(2000*0.05^2)/(25)}`

r=
`√(5)`20*0.05/5=0.44m or 44cm

This is the radius, meaning that the diameter will be twice this number