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(II) A meteorite has a speed of 90.0 $\mathrm{m} / \mathrm{s}$ when 850 $\mathrm{km}$ above the Earth. It is falling vertically (ignore air resistance) andstrikes a bed of sand in which it is brought to rest in 3.25 $\mathrm{m}$ .(a) What is its speed just before striking the sand? (b) How muchwork does the sand do to stop the meteorite (mass $=575 \mathrm{kg}$ ?(c) What is the average force exerted by the sand on themeteorite? (d) How much thermal energy is produced?

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A) $3840 \mathrm{m} / \mathrm{s}$B) $-4.23 \times 10^{9} J$C) $1.30 \times 10^{9} N$D) $4.23 \times 10^{9} J$

13:54

Maria Gabriela Cota Moreira

08:12

Keshav Singh

Physics 101 Mechanics

Chapter 8

Conservation of Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

McMaster University

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

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in this problem, we're going to talk about conservation off energy. So we need to remember that the initial kinetic energy of a system, plus the initial potential energy, is equal to the final kinetic energy because the final potential energy if the mechanical energy is conserved, that is, if the forces that are acting on the system, our concept conservative, how in particular for our exercise, we need to remember that the gravitational, our potential energy is which, minus Newton's gravitational constant times the mass off one of the objects time to mess with the other one divided by the distance between the two object. And besides, we also we're also gonna need the concept of work. So the work exerted on an object is equal to the integral of the force over distance, from the point where the force starts being applied to the force, to the point where the force stops me applied, and it also can be written as the average force times the distance. The attacks, the average force and the average force is defined as one over delta acts times l F uh, the X zero to X, where no taxes your X men is extreme luxury. Okay, Eso Now we can calculate what the exercise asks us. So basically we have a media or that is moving within initial speed V I of 90 m per second with a mass off 575 kg at a height from the surface of the earth off 850 kilometers on and the media or hits the earth. It's the sand off the earth and it is completely stopped by the sand. After traveling a distance of 23.25 m in the sense and our goal in question A is to find what is the final speed off the media or yeah, on here. I'm just gonna use conservation of energy. So have the M V. I squared over to This is the initial kinetic energy minus G am time of the mess of the meteor here, Capital M is the mass of the earth. Divided by the radius of the earth was the, uh, distance between the surface of the earth and the media is equal to, um v f squared over two minus g m am divided by the radius of the earth. Okay, so the EMS can swatch and our goal is to find VF. So that's what I'm gonna do. So VF squared over two is vice squared over two US G capital M times one over r mine is one over R plus age eso What we have is that VF is equal to the square root of ei squared was to g m times one over r minus one over r polis age and a couple of things We need to remember first that the rate is of the earth and even the write it down here. The rate is of the earth is 6.38 times 10 to the sixth meters, while the mass of the earth is 5.98 times 10 to the 24 kg. Finally, the gravitational constant is 6.67. I'm Stan to the miners. 11 Newton's meter squared regular graham squared. So yes is equal to the initial speed which is 90 m per second square was two times 6.67 time Stand to the minus 11 Newtons meters squared per kilogram squared times one over the Raiders of the Earth at 6.38. I'm sent to the 6 m minus one over the radius. Plus, actually, I think it would be better if I just world this in the next line. So I don't have to shrink my number so much. So we have minus one over 6.38 times 10 to the sixth meters. Well, his age and H is off 850 kilometers. So it's 8.5 times sent to the fifth meters. I'm sorry for having written this in two lines, so yeah is equal to 300. I'm sorry. 3800 and 35 m per second. Then in question be our goal is to calculate what is the work exerted by the by the sand over the media or in order to completely force it to a halt. So, uh, the work is gonna be equal to the variation in kinetic energy off the media notice that the initial kinetic energy eyes equal to the initial kinetic energy. But, um, if you square over two while the final kinetic energy, just zero since the, uh instead of calling K, I am gonna call it just K and the final kinetic energy. Okay, Prime is zero Jews since the object is arrest. So the work done is equal to the kinetic energy that was lost. Actually, there is a minus sign here. Eso the kinetic energy that was lost. It's just MV squared over two. A mess is equal to 575 kg. V is 3, 38 135 m per second squared, divided by shoe. So w is equal shoe 4.23 times 10 to the ninth. Jules, this is the work done over the media war in question. See, we have to calculate the average forced that descend exerted over the media. And if you remember the average force times the distance is equal to the work. We know that the distance along which the force was applied is just 3.25 m. So f prime SRF bar is, uh, w divided by D. So that's 4.23 time sent to the nine Jews divided by 3.25 meters. This is what you 1.3 times 10 to the ninth Newton's. Then in question D are going to calculate what is the thermal energy that was lost? Basically uh, what is the thermal thermal energy that's produced? I'm sorry. So the thermal energy, I'm gonna call it Q. Assuming that the all the kinetic energy off the media war becomes converted to thermal energy, then Q is equal to the work that the sun did over the media. And that is equal to 4.23 time. Stand to the ninth, and this concludes our exercise.

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