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Q.24

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 384

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Short Answer

Styrofoam has a density of . What is the maximum mass that can hang without sinking from a Styrofoam sphere in water Assume the volume of the mass is negligible compared to that of the sphere.

Maximum mass that can hang without sinking from Styrofoam sphere is .

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Step by Step Solution

Step 1: Definition of Styrofoam 

Closed-cell extruded polystyrene foam, or XPS, is a trademarked brand of Styrofoam. Blue Board is another name for this foam, which is used for building insulation, thermal insulation, and water barriers.

The polymer polystyrene, with styrene as the repeating monomer, is used to make Styrofoam. Only carbon and hydrogen make up styrene.

Step 2: Expressions for force and mass

Use the expression for buoyant force to determine the required mass.

The buoyant force is expressed as follows:

Here, is density of the fluid and is volume of displaced fluid which is equal to volume of Styrofoam sphere.

For the mass that can hang without sinking, the downward gravitational force must be balanced by the upward buoyant force.

In this case, the net force on the mass is expressed as follows:

Here, is buoyant force is mass of Styrofoam sphere, andis acceleration due to gravity.

Step 3: Calculation of mass

Combine the above two relations.

Here, is mass of the object.

Volume of Styrofoam sphere is,

Mass of the Styrofoam sphere is,

Here, is density of Styrofoam sphere.

Replace with and with in .

Substitute for , for ,for

Maximum mass is

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