Problem Statement
A hydraulic press has a ram of 300 mm diameter and a plunger of 50 mm diameter. Find the weight lifted by the hydraulic press when the force applied at the plunger is 40 N.
Given Data & Constants
- Diameter of Ram, \(D = 300 \, \text{mm} = 0.3 \, \text{m}\)
- Diameter of Plunger, \(d = 50 \, \text{mm} = 0.05 \, \text{m}\)
- Force on Plunger, \(F = 40 \, \text{N}\)
Solution
1. Calculate the Area of the Ram (A) and Plunger (a)
2. Calculate the Pressure Exerted by the Plunger (P)
The pressure in the hydraulic fluid is the force on the plunger divided by its area.
3. Calculate the Weight Lifted by the Ram (W)
According to Pascal's Law, the pressure is transmitted equally throughout the fluid. This pressure acts on the larger area of the ram to lift the weight.
Alternatively, using the ratio of areas:
The weight lifted by the hydraulic press is \(1440 \, \text{N}\).
Explanation of Pascal's Law
Pascal's Law is the fundamental principle that makes hydraulic systems work. It states that a pressure change at any point in a confined, incompressible fluid is transmitted equally and undiminished to all points throughout the fluid.
In this press, the small force of 40 N applied over the small area of the plunger creates a pressure in the fluid. This same pressure then acts on the much larger area of the ram, generating a proportionally larger output force (the weight lifted). The force multiplication factor is simply the ratio of the areas (\(A/a\)), which in this case is 36. This allows a small input force to lift a much heavier load.
