Hydrostatics physics question

[sovankc]

Homework Statement

A girl of mass 40 kg and volume of 40 liter wants to keep her head of volume 3 liter above water surface as she can't swim . how much air in Kg should she fill in her jacket??

Homework Equations

The Attempt at a Solution

mass of girl (m) = 40 kg
volume of girl (V) = 0.04 m^3(meter cube)
density of girl (D) = m / V = 1000 kg/m^3
volume of head (v') =0.003 m^3

let the mass of air in kg be x then

total mass of body = 40 + x
mass of water displaced = 40 + x
volume of water displaced = 1000(40 + x)
then
volume of immersion = V - v' = .04- .003 = .397

therefore from principle of flotation
volume of water displaced = volume of immersion of floating body
40000 + 1000x = .397
x=.397-40000 = -ve value





is my method correct? and as " density of body = density of water " will require extra air to float.

 

[Jhero]

Your method is generally correct, but there are a few things to consider. First, it is important to clarify that the volume of the girl's head should be added to the volume of her body (40 liters) to find the total volume of her body. This would give a volume of 43 liters, or 0.043 m^3.

Next, the density of the girl's body should be calculated using her total volume, not just her body volume. This would give a density of 930.23 kg/m^3, which is slightly less than the density of water (1000 kg/m^3). This means that the girl's body will naturally float in water, without needing any additional air in her jacket.

However, if we want to lift her head 3 liters above the water surface, we do need to add some air to her jacket. To find the mass of air needed, we can use the equation you set up:

volume of water displaced = volume of immersion of floating body
(40 + x) = 0.397

Solving for x, we get x = -39.603 kg. This is a negative value because we are technically removing this amount of mass (air) from the girl's body in order to lift her head above the water surface.

So, to answer the original question, she would need to add approximately 39.6 kg of air to her jacket in order to keep her head 3 liters above the water surface.