- #1
sodr2
- 26
- 0
Homework Statement
With the nose above the water, about 95% of the body is submerged. Calculate the power expended by a 50-kg woman treading water in this position. Assume that the average density of the human body is about the same as water (p = pw = 1 g/cm3 ) and that the area A of the limbs acting on the water is about 600 cm2.
Homework Equations
Bear with me...FB = gVpw <-- force up, due to buoyancy
Fg = gVp <-- force down due to gravity
FD = Fg - FB = gV(p - pw ) <-- net downward force (assuming the object is more dense than water)
Mass of water accelerated per unit time (m) = Avpw
Momentum given to the water per second = mv
^^ these two equations make absolutely no sense to me, but when they are put together:
FR = pwAv2 <-- force produced that should be equal to FD to counter the downward force so you can float, and since the units (density x area x velocity2) turn out to be essentially mass x acceleration (ie a force), $#!t makes sense...
FD = FR = gV(p - pw ) = pwAv2
Rearranged... v = *sqrt* of: gV(p - pw) / Apw
KE/sec = Power generated by limbs, P = 1/2 mv2
Substituting eq'ns for m & v...
P = 1/2 *sqrt* of: [W (1 - pw/p)]3 / Apw
Here W is the weight of the object (W = gVp).
The Attempt at a Solution
First, the question says to assume that density of the body is the same as water... so why is it necessary to do work to remain afloat? In the last equation, if you divide the density of the body and water, it equals 1, and 1-1 = 0, therefore P = zero...