Question

In 1656, the Burgmeister (mayor) of the town of Magdeburg, Germany, Otto Von Guericke, carried out a dramatic demonstration of the effect resulting from evacuating air from a container. It is the basis for this problem. Two steel hemispheres of radius 0.380 m (1.25 feet) with a rubber seal in between are placed together and air pumped out so that the pressure inside is 17.00 millibar. The atmospheric pressure outside is 950 millibar. Calculate the force required to pull the two hemispheres apart.

Answer 1

F = 42325.17 N

Step-by-step explanation:

We are given;

Radius of hemispheres; r = 0.38 m

Inner pressure; P_i = 17 milli bar

Outside Pressure; P_o = 950 milli bar

Now, net pressure; P_net = P_o - P_i

P_net = 950 - 17

P_net = 933 milli bar

From conversion rates, we know that;

1 milli bar = 100 N/m²

Thus;

P_net = 933 × 100

P_net = 93300 N/m²

Surface Area of hemisphere; A = πr²

A = π × 0.38²

Now, formula for pressure is;

P = F/A

Where F is force.

Thus making F the subject;

F = P × A

Plug in P_net and A to get;

F = 93300 × π × 0.38²

F = 42325.17 N