A plastic ball has radius 12.0 cm and floats in water with 24.0 of its volume submerged

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A plastic ball has radius 12.0cm and floats in water with 24.0% of its volume submerged.

What force must you apply to the ball to hold it at rest totally below the surface of the water?

If you let go of the ball, what is its acceleration the instant you release it?

2 Answers

  • ρ— Density of water.

    Buoyant force in the first case when floating = 0.24vρg = the weight of the ball..

    When fully submerged the buoyant force is v*ρg.

    Difference in the upward force is 0.76 vρg.

    Hence a downward force of 0.76(4/3) π 0.12^310009.8 = 53.9 N has to be applied.


    Acceleration at that instant = net force /mass =0.76 vρg/ 0.24vρ.

    = 0.76*9.8/0.24 = 31.03 m/s²

  • 1) Find the volume of the ball

    2) Volume x 24% = submerged volume = displaced fluid. The weight of the displaced fluid = the weight of the ball.

    3) If the ball is totally submerged it will be buoyed upward by a force equal to the weight of the fluid it is displacing – the weight of an equal volume of water. However, it is being held down by its weight. So, the force needed would be the weight of the displaced water – the weight of the ball.

    4) Now we are at F = ma. The force will be the same as the force needed to hold the ball submerged. You need to turn the ball’s weight into its mass; and either use the force found in #3, or use the (weight of the displaced water – weight of the ball) as the net force.

    The ruling idea behind all of this stuff is “When a body is placed in a fluid it is buoyed upward by a force equal to the weight of the displaced fluid.” That’s how stuff floats – from party balloons to battleships.

Problem 76P

Problem 76P

A plastic ball has radius 12.0 cm and floats in water with 24.0% of its volume submerged. (a) What force must you apply to the ball to hold it at rest totally below the surface of the water? (b) If you let go of the ball, what is its acceleration the instant you release it?

Step-by-Step Solution:

Step 1 of 3

Solution 76P

31.0 m/

Textbook: Sears and Zemansky's University Physics with Modern Physics
Edition: 13

Author: Hugh D. Young; Roger A. Freedman; A. Lewis Ford
ISBN: 9780321696861

The answer to “A plastic ball has radius 12.0 cm and floats in water with 24.0% of its volume submerged. (a) What force must you apply to the ball to hold it at rest totally below the surface of the water? (b) If you let go of the ball, what is its acceleration the instant you release it?” is broken down into a number of easy to follow steps, and 55 words. Sears and Zemansky's University Physics with Modern Physics was written by and is associated to the ISBN: 9780321696861. The full step-by-step solution to problem: 76P from chapter: 12 was answered by , our top Physics solution expert on 09/09/17, 04:08AM. This full solution covers the following key subjects: ball, its, Water, must, floats. This expansive textbook survival guide covers 44 chapters, and 8517 solutions. This textbook survival guide was created for the textbook: Sears and Zemansky's University Physics with Modern Physics, edition: 13. Since the solution to 76P from 12 chapter was answered, more than 408 students have viewed the full step-by-step answer.

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