Question

If the human body has an average density of 985 kg/m^3, what fraction of a person is submerged when floating gently in fresh water which has a density of 1000 kg/m^3?

a) 98.5%
b) 99.5%
c) 98.0%
d) 99.0%

Answer 1

Approximately 1.5% of the person's volume is submerged when floating gently in fresh water.

Step-by-step explanation:

When an object floats in a fluid, it displaces a volume of fluid equal to its own volume. The buoyant force exerted by the fluid on the object is equal to the weight of the fluid displaced. To find the fraction of a person that is submerged when floating gently in fresh water, we can use the equation:

FB = ρfluid * Vsubmerged * g

Where FB is the buoyant force, ρfluid is the density of the fluid, Vsubmerged is the volume of the person submerged, and g is the acceleration due to gravity. Since the person is floating gently, the buoyant force is equal to the weight of the person:

FB = m * g

Where m is the mass of the person. Combining these equations, we have:

m * g = ρfluid * Vsubmerged * g

Dividing both sides of the equation by m * g, we get:

Vsubmerged = ρfluid / ρperson

Substituting the values for ρfluid (1000 kg/m³) and ρperson (985 kg/m³) into the equation, we find that the fraction of the person submerged is:

Vsubmerged = 1000 kg/m³ / 985 kg/m³ = 1.015

This means that approximately 1.5% of the person's volume is submerged when floating gently in fresh water.