# 2017.02.02 Homework 13_ Gravitation.pdf - Homework 13...

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Homework 13: Gravitation Due: 11:59pm on Tuesday, April 11, 2017 To understand how points are awarded, read the Grading Policy for this assignment. Understanding Newton's Law of Universal Gravitation Learning Goal: To understand Newton's law of universal gravitation and be able to apply it in two­object situations and (collinear) three­object situations; to distinguish between the use of and . In the late 1600s, Isaac Newton proposed a rule to quantify the attractive force known as gravity between objects that have mass, such as those shown in the figure. Newton's law of universal gravitation describes the magnitude of the attractive gravitational force between two objects with masses and as , where is the distance between the centers of the two objects and is the gravitational constant. The gravitational force is attractive, so in the figure it pulls to the right on (toward ) and toward the left on (toward ). The gravitational force acting on is equal in size to, but exactly opposite in direction from, the gravitational force acting on , as required by Newton's third law. The magnitude of both forces is calculated with the equation given above. The gravitational constant has the value and should not be confused with the magnitude of the gravitational free­fall acceleration constant, denoted by , which equals 9.80 near the surface of the earth. The size of in SI units is tiny. This means that gravitational forces are sizeable only in the vicinity of very massive objects, such as the earth. You are in fact gravitationally attracted toward all the objects around you, such as the computer you are using, but the size of that force is too small to be noticed without extremely sensitive equipment. Consider the earth following its nearly circular orbit (dashed curve) about the sun. The earth has mass and the sun has mass . They are separated, center to center, by . Part A Typesetting math: 77%
What is the size of the gravitational force acting on the earth due to the sun? Express your answer in newtons. Hint 1. What units to select For the force to come out in newtons, all masses and distances used must be expressed in SI units. Note that neither ( ) nor ( ) is in the SI unit of length, which is meters. ANSWER: Correct This force causes the earth to orbit the sun. Part B At the moment shown in the figure of the earth and sun , what is the direction of the gravitational force acting on the earth? The possible directions are displayed in this figure . ANSWER: 3.53×10 22 A B C D E Typesetting math: 77%
Correct As the earth proceeds around its orbit, the direction of the gravitational force acting on it changes so that the force always points directly toward the sun. Part C What is the size of the gravitational force acting on the sun due to the earth? Hint 1. Newton's third law Newton's third law states that if object A exerts a force on object B, then object B must exert a force of the same type on object A. These two forces are equal in size and exactly opposite in direction. Since they act on different objects, these two forces never cancel one another out.

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