Question

A hydraulic lift is to be used to lift a 1900-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

To determine the diameter of the second piston required to lift a 1900-kg weight using a hydraulic lift with a pedal cylinder of diameter 10 cm and weight of 25 kg, use the equation F1/A1 = F2/A2 in determining the force exerted on the pedal cylinder and then calculate the diameter of the second piston using the equation diameter of the second piston = √((F1/F2) * A2) * 2.

Step-by-step explanation:

According to the equation relating force and area in a hydraulic system, F1/A1 = F2/A2, we can calculate the force exerted on the pedal cylinder as follows:

F1 = (F2/A2) * A1

Given that F2 = 1900 kg * 9.8 m/s2 = 18620 N, A1 = π * (10 cm/2)2 = 78.54 cm2, and A2 = π * (diameter of the second piston/2)2

Using the above values, we can solve for the diameter of the second piston:

diameter of the second piston = √((F1/F2) * A2) * 2

Answer 2

here in Hydraulic system the pressure on both sides will remain the same

`P_1 = P_2`

`(F_1)/(A_1) = (F_2)/(A_2)`

`(mg)/(\pi*(10^2)/(4)) = (Mg)/(\pi (d^2)/(4))`

`(25)/(10^2) = (1900)/(d^2)`

`d = 87.2 cm`

so its diameter is 87.2 cm