VDU_Physics_2_009

# ## Physics 2.-  Pressure

Javier Montenegro Joo

## jmj@VirtualDynamics.Org

Pressure.-

(1) A force of 500 N is applied to the small piston of a hydraulic press whose diameter is 5 cm. determine the diameter of the large piston so that it raises a metallic ball of 1200 kg.

Solución.-

In the hydraulic press the liquid (usually oil) in contact with both pistons transports the pressure exerted on the small piston to the large one. Since the pressure is the same in all the liquid and, the pistons have different areas the resulting forces are different.  In this way a small pressure applied to the small piston generates in a large force on the large piston. (2) A cylindrical vertical tank containing compressed gas remains sealed by a piston of 2 kg and the weight of two bricks of 9 kg each, which are resting on the piston. The cross-section area of the piston is 8.0   cm². Determine (a) the pressure of the gas inside the tank and (b) the gauge (manometric) pressure of the gas inside the tank.

Solution.-

The gas is retained inside the cylinder by to the pressure of the piston and that of the two bricks resting on it and, that of the atmosphere. (3) The sketch shows a hydraulic press made of two cylindrical branches of diameters D and 3D, respectively. The devise uses two immiscible liquids whose densities are one the double of the other. Bearing in mind that the system is in equilibrium, find the mass m of the small piston as a function of the other parameters. Solution.-

The weights of both pistons exert pressure on the liquids below them. Since the system is in equilibrium, the pressure must be the same at the bottom of both branches. Start by calculating the pressures due to the cylinders resting on top of both liquids: 