Question

A hydraulic press has a ram of 30 cm diameter and a plunger of 4.5 cm diameter. Find the weight lifted by the hydraulic press when the force applied at the plunger is 500N.​

Answer 1

Given,

Diameter of ram = 30 cm = 0.3m

Diameter of plunger = 4.5 cm = 0.045m

Force applied at plunger = 500N

To find,

The weight lifted by the hydraulic press.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Here, we have to use the Pascal's law, which states that :

Force/Area = constant

Here,

Area of ram = π/4 × (0.3)²

Area of plunger = π/4× (0.045)²

Force of plunger = 500N

Force of ram = x

So,

500/[π/4×(0.045)²]= x/[π/4×(0.3)²]

500/(0.045)² = x/(0.3)²

x = 500×0.3×0.3/0.045 × 0.045

x = 45/0.002025

x = 22222.22

Lifted weight = 22222.22 N = 22.22 kN (approx)

Hence, the lifted weight is 22.22 kN