Question

A hollow plastic sphere is held below the surface of a freshwater lake by a cord anchored to the bottom of the lake. The sphere has a volume of 0.700m3 and the tension in the cord is 840N. What is the mass of the sphere?

Answer 1

A.) The buoyant force is the weight of the fluid displaced. . The mass of the fluid displaced is the the density of water x the volume of the water displaced. Since the sphere is fully submerged in the water, the total volume of the sphere is the volume of the water displaced. Hence:

The density of freshwater is (1 x 10^3kg/m3)

B.) If you were to make a free body diagram of the sphere, there will be an upward buoyant force and a downward force of tension on the sphere, and a downward force of its weight. We can take the sum of the forces in the y direction to help find the mass:

(The sphere is not moving)

Solve for mass, m

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C.) If the cord breaks, that means the only forces acting on the sphere will be its downward weight and upward buoyant force. The equation for the volume of an object submerged is:

First we have to find the density of the sphere before we can find the volume submerged:

Now we can use this value for our previous equation:

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