What force F must be applied to the small

piston to maintain the load of 49 kN at a
constant elevation?

To determine the force F required to maintain a load of 49 kN at a constant elevation, we need to consider the principles of hydraulic systems.

In a hydraulic system, the force exerted on a smaller piston is transmitted to a larger piston through an incompressible fluid (usually oil or hydraulic fluid). The two pistons are connected by a common fluid-filled pipe or tube.

Based on the principles of Pascal's law, the pressure exerted in a hydraulic system is the same throughout, regardless of the cross-sectional area of the pistons. Therefore, we can use the formula:

Force = Pressure × Area

Here's how to calculate the force F on the small piston:

1. Determine the pressure exerted on the small piston. The pressure is the same throughout the system, so we can calculate it by dividing the load by the area of the larger piston.

Pressure = Load / Area of larger piston

2. Calculate the area of the smaller piston using its diameter or radius.

Area of smaller piston = π × (radius of smaller piston)²

3. Substitute the values into the formula:

Force = Pressure × Area of smaller piston

By following these steps, you can calculate the force F required to maintain the 49 kN load at a constant elevation.