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(II) How much work would be required to move a satelliteof mass $m$ from a circular orbit of radius $r_{1}=2 r_{\mathrm{E}}$ aboutthe Earth to another circular orbit of radius $r_{2}=3 r_{\mathrm{E}} ?$$\left(r_{\mathrm{E}}$ is the radius of the Earth.) \right.

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$\frac{G M m}{12 r_{E}}$

Physics 101 Mechanics

Chapter 8

Conservation of Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

University of Michigan - Ann Arbor

University of Washington

Simon Fraser 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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Derive an expression for t…

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A spacecraft moves around …

02:58

A 200.-kg satellite is in …

00:49

Energy required to move a …

00:45

01:03

How much work is required …

00:42

How much work is performed…

02:00

An object of mass $m$ is i…

06:05

A $3000-\mathrm{kg}$ space…

So we have a satellite and it is an A radius off or run, which is two times the radius of the earth right here. And it is pushed to another radius are too, which is three times the beauteous of birth. Satellite is moving from disposition to this position and we need to find out Ah, what is the work done to achieve this change? Basically, autumn of the satellite from a radius of two Ari to introduce a theory and that height now, according to the work energy cure, um, work external is equals to the change off potential energy and the change of kinetic energy board energies will change here, which is basically calls to the change off mechanical energy off the satellite. Now we can find out the expression for the mechanical energy of satellite so we know that the kinetic energy is equals to have and b squared and then we have the potential Energy is equals two negative g m m. By our now, This kind of energy is also equals to have and the velocity of a second in this orbit is G mass off the earth, divided by our. So if you add this, we'll get kinetic less potential energy. This equals two have g m m by our minus g m and by our So that should give you the mechanical energy is minus have g m m my r So that is the kinetic and potential the total mechanical energy off the satellite. So we know from the previous equation that the work external is equals to the change off the mechanical energy so we can find out the mechanical energy change because we know that he is equals two minus half g m m by our so which implies that Delta E should be equals two minus 1/2 g m m by r, which is the initial minus minus, have she em? And by our so this should be the final. And this would be the initial so that still today. So delta easy cause you're minus half GM and by our final minus minus half gmm by our initial so we can solve that further should be equals two have g m m by our initial minus have g m m by our final just rearranging the minus minus becomes place here now reporting the actual values here, which is equals to have G m mm bye to Ari. That should be equals two to Ari, minus half g m m by three rd. See, if you saw that, you will get a g m and by twelves are you So that is the mechanical energy or the work done for moving a satellite from are one Witches are too ari too. All three are

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