Problem

A negative pressure of 25.0 atm can sometimes be …

03:13

Problem 79 Hard Difficulty

(a) How high will water rise in a glass capillary tube with a 0.500 -mm radius? (b) How much gravitational potential energy does the water gain? (c) Discuss possible sources of this energy.

Answer

(a) $h_{\text {water }}=0.030 \mathrm{m}$
(b) $P E=6.93 \times 10^{-6} \mathrm{J}$
(c) Surface tension.

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Physics 101 Mechanics

College Physics for AP® Courses

Chapter 11

Fluid Statics

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Video Transcript

We'll ask how high water rise in a glass capital early too, with a 0.5 millimeters radius. And then we're asked how much gravitational potential energy does the water gain and discuss possible sources of that. So we have our capital ery and we can look up the surface tension off water serial point 07 to 8 million Newtons per meter. The contact angle of water glass is zero degrees so we can use our former like here for the height and the capital Eri So we have two times the surface tension of water Times Co sign of zero is one the density of water g and then the radius of the capital Eri plugging those numbers into the calculator and we get that that is 2.97 senators Now we want to figure out what the the potential energy stored in that ISS. So the potential energy it's simply the mass, the weight of the fluid and then kinds its center of mass which is at H over too. So the mass is the density times volume and we can write the volume as pi r squared h Then we have another age here. So we get eight square and then we get roti all over too, so we can plug in and start plugging in some numbers here and we had have are we have a TSH eight squared. We wind up with four gamma square co sign squared of data over density ofwater, square times gravity square times the radius squared And then we have pie r squared density ofwater kinds gravity You can start cancelling some things out So we have a four to that becomes a two The surface tension squared pi We have our square than the numerator and denominator Wait Oh, ro w squared in the denominator and rolled up the numerator So we get really w the denominator. We have g in the numerator and tease square the denominator. So we get in the denominator And then we left over with our co sign squared. Oh, data. Now you can then start plugging into actual numbers to our formula here and get density of water, gravity, surface, tension of water. And then so we get this value and then we start doing the units get pretty hairy over here so we can start doing a little unit analysis over here. So we have meter squared, um, uneaten squared per meter squared. So newton is a kilogram meters per second squared. So we get kilograms square kinds, meter squared over seconds to the fore and then provided by meters squared. And then down here we get a mutinous cube provided by kilograms, and we get a second squared, divided by meters. And so you see that these this cancels with way. Get three theaters down here, um, three here that would cancel out we get a kilogram here, cancels with one of the kilograms up here. Second squared, so appears that we get second square down new denominator. And what we're left over with is a unit of jewels, which is Newton's times meters. So kilogram, meters squared, second square. And if we calculate our number of fear, number your value. We get 3.4 times 10 to the minus six with his then 3.4 micro Jules. Now where does that energy come from? Well, there's a reduction in free surface area when the water what's the capital ery? And that reduction, um, basically allows the energy to decrease in the surface area so we can increase the potential energy in the water

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