Buoyant Force?

Classical Mechanics Level 3

The bottom of a swimming pool is made of metal (for some strange reason). A solid closed metal cylinder of height $2 \, \text{m}$ and radius $1 \, \text{m}$ has its bottom face welded to the bottom of the pool. The rest of the cylinder is surrounded by water. The water surface is $1 \, \text{m}$ above the top of the cylinder.

What is the net vertical force exerted by the water on the cylinder (in Newtons)? If the force is downward, give your answer as a negative number. If the force is upward, give your answer as a positive number.

Details and Assumptions:
1) Gravity $g = 10 \, \text{m/s}^2$ downward
2) Water density $\rho_w = 1000 \, \text{kg/m}^3$
3) Neglect the air pressure outside of the pool
4) The weld is closed and water-tight

The answer is -31415.93.

1 solution

Parth Sankhe
Jan 4, 2019

Since the bottom is not exposed to the water, the only vertical force acting on it will be by the pressure of water on the upper face. (The forces on the curved surfaces will be horizontal)

$F=P\cdot A$

$=(hdg)\cdot (πr^2)$

After putting in the values, this comes out to be $10,000π$ . Then we put a negative sign as the force is downwards, and the final answer is $-31415.9$ newtons.

Buoyant Force?

The answer is -31415.93.

1 solution

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