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 .
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.
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.
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
It's possible to use the ideal-gas law to show that the density of the earth's atmosphere decreases exponentially with height. That is, , where is the height above sea level, is the density at sea level (you can use the Table value), and is called the scale height of the atmosphere.
a. Determine the value of .
Hint: What is the weight of a column of air?
b. What is the density of the air in Denver, at an elevation of ? What percent of sea-level density is this?
Geologists place tiltmeters on the sides of volcanoes to measure the displacement of the surface as magma moves inside the volcano. Although most tiltmeters today are electronic, the traditional tiltmeter, used for decades, consisted of two or more water-filled metal cans placed some distance apart and connected by a hose. FIGURE shows two such cans, each having a window to measure the water height. Suppose the cans are placed so that the water level in both is initially at the mark. A week later, the water level in can is at the mark.
A. Did can move up or down relative to can ? By what distance?
B. Where is the water level now in can ?
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