A hydraulic jack having a ram 200 mm in diameter lifts a weight W= 40 kN under the action of a 25 mm plunger. What force is required on the plunger to lift the weight

To solve this problem, we need to use Pascal's law, which states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.

Here's the step-by-step solution:

1. First, we need to calculate the area of both the ram and the plunger. The formula for the area of a circle is πr².

   For the ram: Diameter = 200 mm, so radius = 200/2 = 100 mm = 0.1 m Area of ram (Ar) = π * (0.1 m)² = 0.0314 m²

   For the plunger: Diameter = 25 mm, so radius = 25/2 = 12.5 mm = 0.0125 m Area of plunger (Ap) = π * (0.0125 m)² = 0.00049 m²

2. According to Pascal's law, the pressure applied on the plunger will be the same as the pressure on the ram. So, we can set up the equation as follows:

   Pressure on plunger = Pressure on ram (Force on plunger / Area of plunger) = (Force on ram / Area of ram)

3. We know the force on the ram (which is the weight W it lifts) is 40 kN = 40000 N. Substituting the known values into the equation:

   (Force on plunger / 0.00049 m²) = (40000 N / 0.0314 m²)

4. Solving for Force on plunger, we get:

   Force on plunger = (40000 N * 0.00049 m²) / 0.0314 m² = 620.38 N

So, a force of approximately 620.38 N is required on the plunger to lift the weight.