A pine board 1 m long, 2 dm wide, 10 cm thick floats on the surface of the water.

A pine board 1 m long, 2 dm wide, 10 cm thick floats on the surface of the water. Calculate the Archimedes force acting on the board and the depth of its immersion in water

Given:

a = 1 meter – the length of the pine board;

b = 2 decimeters = 0.2 meters – the width of the pine board;

c = 10 centimeters = 0.1 meter – the thickness of the pine board;

ro = 1000 kg / m3 (kilogram per cubic meter) – water density;

ro1 = 520 kg / m3 – density of pine;

g = 10 Newtons per kilogram is the acceleration of gravity.

It is required to determine A (Pascal) – the Archimedean force acting when the board is immersed in water and h (meter) – the immersion depth.

Let’s find the volume of a pine board:

V = a * b * c = 1 * 0.2 * 0.1 = 0.02 m3.

The mass of the board will be equal to:

m = V * ro1 = 0.02 * 520 = 10.04 kilograms.

Then the force of gravity acting on the pine board will be equal to:

F = 10.04 * 10 = 100.4 Newton.

Since the board is in balance, the Archimedean force will be equal to the force of gravity:

A = F = 100.4 Newton.

The depth of the immersed part will be equal to:

h = A / (g * a * b * ro) = 100.4 / (10 * 1 * 0.2 * 1000) = 100.4 / 2000 = 0.052 meters (5.2 centimeters).

Answer: the Archimedean force will be equal to 100.4 Newton, the immersion depth will be 5.2 centimeters.