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QA › Math › A flat slab of styrofoam, with a density of 32 kg/m^3, floats on a lake. What is the minimum volume the slab must have so that a 42 kg boy can sit on the slab without it sinking?

A flat slab of styrofoam, with a density of 32 kg/m^3, floats on a lake. What is the minimum volume the slab must have so that a 42 kg boy can sit on the slab without it sinking?

Solution:

The density of Styrofoam is 32kg/m3

Since it’s on a lake, then the density of water is 1000kg/m3

Buoyant Force = the boy’s weight + mass of ice

V (ρwater – ρice) = m

V= m/(ρwater-ρice)

Thus, V=42/1000-32= 0.0434m3

When the magnitude of the upward force exerted by the water on the object is less than the weight of the object, the object will sink into the water. When the weight of the object is equal to the upward force exerted by the water, the condition represents the flotation of the object.

Math

3 years ago

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