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Suppose that you release a small ball from rest at a depth of 0.730 m below the surface in a pool of water. If the density of the ball is 0.350 that of water and if the drag force on the ball from the water is negligible, how high above the water surface will the ball shoot as it emerges from the water? (Neglect any transfer of energy to the splashing and waves produced by the emerging ball.)

User Junvar
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2 Answers

5 votes

Final answer:

The ball subjected to a buoyant force in water with negligible drag will rise but will not shoot higher than the depth it was released from. The rise is due to the work done by the buoyant force while submerged, and the maximum height achieved will be less than or equal to the depth of 0.730 m.

Step-by-step explanation:

The question asks how high above the water surface a ball will shoot as it emerges from the water, given that its density is 0.35 that of the water and there is negligible drag force acting on it.

To solve this, we use the conservation of mechanical energy, assuming energy is only exchanged between gravitational potential energy and buoyancy, and knowing that the buoyant force will do work on the ball to propel it upwards.

With the ball's density being 0.35 of water's, the buoyant force will exceed the gravitational force while the ball is submerged. However, the buoyancy vanishes as the ball emerges, and only the kinetic energy acquired underwater propels it upwards. The ball will not reach a height greater than the depth from which it was released due to losses when transitioning between mediums and the additional gravitational potential energy needed to be acquired above water.

So the answer is: the ball will not shoot above the water surface, and its maximum height will be less than or equal to 0.730 m.

User Rickvdbosch
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6.1k points
2 votes

Answer:

21.8 m

Step-by-step explanation:

Net force on the ball inside water

= Buoyant force - weight of ball

= mρg - mdg

where ρ is density of water and d is density of ball

= m ( ρ - .35ρ ) g

This force acts on the ball upto distance .73 m so work done by force will be equal to kinetic energy acquired by the ball.

m ( ρ - .35ρ ) g x .73 = 1/2 mv²

10³ ( 1 - .35 ) x g x .73 = 1/2 mv²

v² = 10³ x .65 x 9.8 x .73 x 2

v² = 9300

After emerging from water , buoyant force stops acting on it.

It will stop at height such that

1/2 mv² = mgh

v² = 2gh

h = v² / 2g

9300 / 2 x 9.8

= 21.8 m

User Rebagliatte
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