A cubic block of side length d is in a water container as shown in the...

A cubic block of side length d is in a water container as shown in the figure. Only half of the block is immersed in water and the block is being held by a rope attached to the bottom of the container. The block is made of wood with density ρ0. A) Find the tension on the string. B) If the container is fill with water up to a height of 1.5 m, calculate the pressure at the bottom of the container

Solutions

Expert Solution

The weight of the block W = mg = d3 g. The weight is in downward direction.

The volume of the block inside the water is half of total volume. Vinside = d3 / 2

The buoyant force acting on this block is B = Vinside x x g = d3 g / 2 and is in upwards.

The tension T in the string is acting in downward direction on the block.

The block is at rest. Hence the buoyant force is balanced by weight and tension.

d3 g / 2 = d3 g + T

T = ( /2 - ) d3 g

b) The hydrostatic pressure at a depth h from the surface of water is P = h g

P = 1.5 x 1000 x 9.8 = 14700 Pa (g=9.8 m/s2)

_____________

If the atmospheric pressure Po is included then the absolute pressure is PA = Po + P

PA = 1.01 x 105 + 0.147 x 105 = 1.157 x 105 Pa

genius_generous answered 1 year ago

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