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$\bullet$ White dwarfs and neutron stars. Recall that density is mass divided by volume, and consult Chapter 0 and Appendix $E$ as needed. (a) Calculate the average density of the earth in $g / c m^{3},$ assuming our planet to be a perfect sphere. (b) In about 5 billion years, at the end of its lifetime, our sun will end up as a white dwarf, having about the same mass as it does now, but reduced to about $15,000 \mathrm{km}$ in diameter. What will be its density at that stage? (c) A neutron star is the remnant left after certain supernovae (explosions of giant stars). Typically, neutron stars are about 20 $\mathrm{km}$ in diameter and have around the same mass as our sun. What is a typical neutron star density in $\mathrm{g} / \mathrm{cm}^{3} ?$

$5.48,1.12 * 10^{6}, 4.7 * 10^{14}$ grams per cubic centimeters respectively,

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

Rutgers, The State University of New Jersey

University of Washington

McMaster University

Lectures

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Okay, so doing tractor on problem 19. So, for a has us calculate the average density of earth assuming that the sphere So this is the mast over volume. If we assume it's a sphere that you can express this volume just in terms of grades. So the value of spheres for thirds Aye. Our cute with this being the radius of earth in the mass of earth. So now we can just give all the numbers we need in Prague. Listen, So the density for the mass we have 597 times, two to the 24 kilograms. So we were asked to get an answer and grams per centimeter cubes. So let's go ahead and convert this two grains by multiplying 5,000 grams. Because it's 1,000 grams per one kilogram. Who's well can't allow There behind the mass. Ingram's up top on bottom, we have our 4/3 ty, and now we just need to get our radius, which was 6.38 times 10 to the sixth. Need it? So now this is in meters. But again, we wanted our answer consuming his huge suppose convert this right here by multiplying by 100 centimetres her meat burger in those council out and then this radius is cute. So now we can plug this hole thing in our capital Letter B C average density of earth. Assuming it's a speeder would be five for no grams Personal meter. Cute. Perfect. So now it says in fine between years, our sun will end up as a white door about having same massive with us now, but the radius will be reduced to you Radius White door rummy returns to 15,000 competence. Okay, so we want to find the mass of the sun or the density of the sun. Now when it becomes a wife who works at this so we plug into our the equation here Mrs Again assuming for a sphere 4/3 pi r cubed Let's plug, whistle And now getting are numbers. We have orne point nine Sorry, that that was a zero is 1.900 times turning to the 30 kilograms for the mass of the sun. Let's convert that to dreams. And now let's divide this by our 4/3 by the radius again was 15,000 kilometers and we want to convert that to silks sorry, this is really the dying there. So our radius is this divided by two on. Then we need to multiply it by 1,000 meters per one kilometer and then we need to convert from meters, centimeters centimetres for one neither. And the whole thing is cute. So it looks like a lot of stuff. But our calculator is strong and can do it all the way. We see that this comes out too long on one times 10 to the sixth creams for centimeter cubes of very much Morgan's in the earth. So now for Parsi, let's go once toe even farther. After the sun collapses and supernova, it will become a neutral star with the diameter you glued 20 kilometers, so was plugged all this into our equation again. Mass is the same still and convert to grams all over on her pie factor. And now, instead of 15,000 kilometers for the damage. He's 20 but I'm too to get to the radius and now multiplied by 1,000 to convert two meters and the north supplied by 100 to get to seven years and cue it all. Once we plug all of that into your calculator. We see that the neutron star density is now 4.7 times 10 to the 14 grains per cent. Beer cubes so much, much higher even in the white Dorf very, very dense stuff.

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