What Force Keeps a Submerged Rubber Ball in Equilibrium?

[TheNextOne21]

Homework Statement

Rubber ball filled with air has a diamter of 25.0 cm and a mass of .540 kg. what force is required to hold the ball in equilibrium immediately below the surface of water?

Homework Equations

anyone want to help me out with an equation here?


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[fatra2]

Hi there,

From Newton's second law of motion, an equilibrium is define as all the force acting on the object cancel each other. Written in an equation, it becomes:
$$\sum \vec{F} = 0$$

In your case, you can easily drop the vector form, since all the forces acting will be vertical:
$$\sum F = 0$$

You need to dfine which forces are acting on the ball.

By the way, whether the ball is keep just below the water' surface or in great depth, the force required will be the same.

Cheers

 

[TheNextOne21]

so the weight of the ball = the buoyant force necessary to keep the object in equilibrium?

if so the answer would be 5.4 which would be different from the answer sheet.

 

[fatra2]

Hi there,

You seem to be missing one force acting on the ball. Archimede's principle says that an object immerge in a liquid is buoyed up by a force equal to the weight of the fluid displaced by the object.

Therefore, three forces act on the ball: the weight of the ball, the archimede's force, and the force you develop to keep the ball in equilibrium.

Cheers