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Which of the following statements are true for a satellite in outer space orbiting the Earth in uniform circular motion? Select two answers. (A) There are no forces acting on the satellite.(B) The force of gravity is the only force acting on the satellite.(C) The force of gravity is balanced by outward force of the object.(D) The mass of the satellite has no effect on the orbital speed.

(B) and (D)

Physics 101 Mechanics

Chapter 7

Uniform Circular Motion, Newton’s Law of Gravitation, and Rotational Motion

Gravitation

Dynamics of Rotational Motion

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and this problem. We're gonna talk about the gravitational work, so consider that we have a planet and we have a satellite. We're actually in the object that rotates around the planet. A circular motion? Yeah, with radius R. So we know that the net force necessary to bring an object to a circular motion the centripetal force must be equal to M v squared over R. This is the net centripetal force on the object. And we know that the force that acts on a non object with the gravitational force is equal to g times the mass of the object and times the mass of the planet capital in divided by r squared. So notice that we can cancel out the EMS and one of the ours, such that V is equal to the square root of capital G m divided by our Okay, So this is the orbit velocity of a satellite around the planet or a planet around the star, etcetera. And based on this brief review, we're gonna answer our problem. So basically, what we have are four options for us, and we have to consider satellite orbiting around the earth in a circular motion in a uniform circular motion. And okay, so we have to select two out of the four alternatives that the exercise gives us. So first, let's analyze alternative eight. Alternative A suggests that there are no forces whatsoever acting on the satellite. Now, this cannot be true. Notice that the satellite is moving in a circular motion. Okay, so the satellite is moving in a circular motion and in order to move in a circular motion, there must be a net force that is responsible for changing constantly changing the direction off the movement off the satellite. So question A is not ah, the correct answer. Then in question be the exercise cells that the Onley force that acts on the satellite is a gravitational food. Well, assuming that the satellite is on the orbit of the earth and that all the gravitational forces that come from other planets and the sun are very small compared to the force of the earth exerts over the object And considering that the orbit is circular, then we can see with confidence that the Onley force acting on the satellite is the gravitational force. So yes, this is correct. So these correct. Let's analyze, See, see tells us that the force of gravity is balanced by a force that is exerted by the objects. So a situation that would be like this notice that in this case, if the force of gravity were balanced by the force exerted by the object itself, um, then the net force would be zero. And the object could not be in circular motion for the same reason, as they told you in item eight, because circular motion requires a total net force a centripetal net force. So this cannot be the alternative also, and objecting out, um, exert force on itself at least not in order to change the position of its center of mass. Okay, so, uh, and considering also that this is a region object, of course. But this cannot be all right. Alternative. So this is not correct. Then let's analyze turned to dee, which suggests that the velocity v off the satellite around the earth does not depend on the math, the math. I'm sorry. And we know that the orbital velocity is equal to the square root of G times the mass of the planet in this case, the mass of the earth divided by R squared. So notice that nowhere in this equation the the mass off the satellite appear. So yes, it's true. The velocity does not change does not depend on the massive satellite. It only depends on the gravitational constant of the mass of the earth and the distance between the satellite and the center of the earth. So our answers are be and deep.

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