Universal Gravitation Quiz

Rishi Garg Physics, 6th Period Mr. McQueen 13 February 2008

Universal Gravitation Quiz 1) I cannot infer from this relationship that the moon’s mass is 1/6 of Earth’s mass. I know this by examining the formula for gravity: g= GMr2. Let’s say that Earth’s gravity and its mass both had a value of one. According to the proposition, the moon’s gravity would be 1/6, as well as the mass. Since G would be the same in each equation, this would only hold true if the radii of both the bodies were the same. However, we know that the moon is much smaller than the earth, so it cannot be true. 2) The scam artist should buy gold at the higher altitude. Weight is defined as the product of an object’s mass and the gravity acting on the object. On Earth, the center of gravity’s pull is the center of the earth. Therefore, as the gold gets farther away from the earth’s center, the force of gravity becomes weaker. In turn, as the force of gravity becomes weaker, the weight of the gold decreases. At a higher altitude, the scam artist would be able to buy more gold for a cheaper price, although it is likely that the price difference would be negligible. 3) The satellite that is twice as far away from the star as the other satellite has a mass that is four times as large as the other satellite. This can be shown using the formula for the force of gravity: Fg=Gmambd2. Let’s say that the force of gravity and the mass of the star both have a value of one. The closer satellite has a mass of value one as well, and has a distance value of one. We can cancel G out because it appears the same in both the satellites’ equations. Now, if we double the distance, to make it two, we have to multiply the mass of the farther satellite by four to keep the force of gravity at one. 4) The correct answer is D: the earth would continue to circle in its usual orbit. This is because the orbit of the earth is dependent on the gravitational pull of the sun, which would only change if the sun’s mass changed. If the sun collapsed to become a black hole, the mass would remain the same; only the size would change. Since the earth is far enough away from the sun or black hole, the gravitational pull would remain the same, keeping it in its regular orbit. 5) Gravity does not increase the speed of the second cannonball because is it in free fall at terminal velocity. According to the question, the cannonball is fired just fast enough so that the curvature of its fall

matches the curvature of the earth. Therefore, it will never touch the ground, and since the only force acting on it is gravity, it is in free fall. Its trajectory is completely horizontal, so gravity cannot increase its velocity because it is never falling toward the ground. It will continue to “fall” or orbit around the earth at a constant velocity.