Problem

$\bullet$ Shear forces are applied to a rectangul…

02:41

Problem 14 Easy Difficulty

$\bullet$ Effect of diving on blood. It is reasonable to assume that the bulk modulus of blood is about the same as that of water $(2.2 \mathrm{GPa}) .$ As one goes deeper and deeper in the ocean, the pressure increases by $1.0 \times 10^{4}$ Pa for every meter below the surface. (a) If a diver goes down 33 $\mathrm{m}$ (a bit over 100 $\mathrm{ft} )$ in the ocean, by how much does each cubic centimeter of her blood change in volume? (b) How deep must a diver go so that each drop of blood compresses to half its volume at the surface? Is the ocean deep enough to have this effect on the diver?

Answer

a) $-1.5 \times 10^{-4}$
b) NO

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Physics 101 Mechanics

College Physics

Chapter 11

Elasticity and Periodic Motion

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Video Transcript

in this problem, we're going to use the law that the change in volume is equal to negative change in pressure times the initial volume over the book module us. And in this problem we're told that the change in pressure is equal to 1.0 times 10 to the fourth Pascal's premier times of death. Because the pressure decreases this much for every meter we go down. And so when we plug in this value for Delta P looking India's 33 meters, which is a value, they give us the initial volume in the book module ISS, which they also give us we get Delta V is equal to negative 1.0 times 10 24 Pascal's demeanors times 33 meters. You'll see this meters and this meters will cancel. Now I have to multiply this by V nine, which is 1.0 centimetres cubed, and we're going to divide by the book Vangelis, which is 2.2 times 10 to the nine scales, and you'll see this pastels and this Pascal's will cancel and our final answer will be in cubic centimeters. Plugging this sense of the calculator, we get negative 1.5 times, 10 to the minus for cubic centimeters. And that's the change in volume that one centimeter cubes of your blood experiences under 33 meter deaths change in the ocean. Pardon me? We're giving that Delta V. Overby not is equal to 1/2 since we're told that the one centimeter Q blood has to go to half its value. So this gives Delta P when you plug it into this formula here. This gives that the change in pressure, his ego to the bulk modules divide by two which in this case is 1.1 times 10 to the nine Pascal's. And so now we can go back to this Got here flooding the delta P. We just found in the sulfur the death that we must be a When we do that, we get death is equal to 1.1 times 10 to the nine over 1.0 times 1.0 10 to 4 and these Aaron SA units. So the answer is gonna be in meters and it's that many meters and this is over 100 kilometers, and the deepest the ocean gets is about a factor of 10 less than that so this is deeper than the deepest spot on the ocean. So no matter what, you could never get your blood to go to half its size. But that doesn't mean it's still not dangerous to go to that depth anyone's, so that's the fun.

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