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Catch a piece of a comet. The Stardust spacecraft was designed to visit a comet and bring samples of its material back to the earth. The craft is 1.7 $\mathrm{m}$ across and has a mass of 385 kg. In January 2004 , from a distance of $237 \mathrm{km},$ it took the photograph of the nucleus of comet Wild shown in Figure $6.30 .$ The distance across this nucleus is $5 \mathrm{km},$ and we can model it as an approximate sphere. since astronomers think that comets have a composition similar to that of Pluto, we can assume a density the same as Pluto's, which is 2.1 $\mathrm{g} / \mathrm{cm}^{3} .$ The samples taken were returned to earth on Jan. $15,2006 .$ (a) What gravitational force did the comet exert on the spacecraft when it took the photo in the figure? (b) Compare this force with the forcethat the earth's gravity exerted on it when the spacecraft was on the launch pad.

(a) 6.28 $\times$ 10$^{-5}$ N (b) 3773 N

Physics 101 Mechanics

Chapter 6

Circular Motion and Gravitatio

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

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okay, and problem 50 treat. We, um I have discovered it, and we're looking at it from, Ah spacecraft. So I wrote a spacecraft to do here. Not sure what spacecraft looked like, but it's Joel Wings, for example. In the trust her it's not wood spacecraft the click. That's what it's gonna be on my drawing. We know a lot of information about those two things. I'll just try down the ones that we will find useful in this problem. So the mass of the spacecraft called someone who's 385 kilograms. We don't have the mass off the comet, but we can extract it from the density. Same thing as we didn't problem 49. So let's do this right now. We know that masses density times, the volume and the problem. They say we can approximate this coming as a sphere, so fear is different. Atmosphere is four pi r cubed over dream, and so it's just draw. This is a sphere instead. The regis are too is um so the distance across is about five commoners, so so that the radius is 2.5 kilometers, or 2000 and 500 meters and the density. Hey, is 2.1 grams persons your square. And as we didn't create in the brotherhood 49 this two dozen 100 kilograms premieres Great. So it's calculate the mass of this. Calm it down. Mess is want 0.37 times tend to the 14 kilograms. Prove meters Q Yeah. Excuse me. Just killed grams. So we get the massive comet and the mass of spacecraft when we should be able to you and to find the gravitational attraction between both. Which is the goal of this problem. Um, one thing we'll need for that it's also the distance between both no cold bits are we know this distance is 237 commoners. Great. So F g is big G times and one times into over r squared. And so we have a whole we need here, but 6.6742 times 10 to the minus 11 and one is try and get in 85 kilograms. Two. I should have freedom this into here as well. And two is this number, which I want to write because it doesn't fit my question with its one point treat. Seven times 10 to 14 kilograms and then R squared. Well, that would be 237 kilometers. It's great. And if I put those numbers on my calculator, I get final force of 6.28 times, tempted to minus five Newtons now and be, um, Dupin greens look different. You want to know the craft Henschel pull of the earth of the spacecraft when it was on the surface of the earth. And so but we can use. Here is the shortcut of using J equals MG because this is valued and the surface of the earth and then get dream Girl. You have kilograms times 9.8 meters per second squared, and that is Tree 100. Consider me 373,770 Tree Newton's or s different. I can draw here So a tree doesn't 700 Senator Newton's or 3.77 times 10 to the Trish Newton's as they put in the manual

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