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Physics 102-002, Mar 7 Announcements Exam 2 graded –Average = 71.4 –Standard Deviation = 15.8 –High score = 96 –Median score = 72 Exam 2 corrections due Wednesday, March 21 –Typed –Include copy of original answer sheet –Give and explain correct answer –Give reference (a page number in the text or the date of the lecture notes) for the correct answer –Turn in hard copy or by email. WebAssign – –Chapter 8 and 9 due Wednesday, March 21 Picture: International Space Station in orbit around Earth If these things aren’t done, you don’t get credit

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Chapter 9 Gravity The Universal Law of Gravity The Universal Gravitational Constant, G Gravity and Distance: The Inverse-Square Law Weight and Weightlessness Skip pgs 168-178

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The Universal Law of Gravity Center of Mass Applet 2Center of Mass Applet 1 Massive objects exert a force on each other that pulls them toward each other. We call this “force of attraction” GRAVITY, or the “gravitational force”. The gravitational force is the same on both objects. There can be more than 2 objects involved. For example the solar system has 9 planets (give or take), and the gravitational attraction is the same on all of them, directed toward the center of mass of the solar system. Actually, every body in the universe attracts every other body. m1m1 m2m2 F - F d

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The Universal Law of Gravity Since Isaac Newton, we’ve known that the gravitational force is directly proportional to the mass of both objects, and inversely proportional to the square of the distance between them: m1m1 m2m2 F - F d Force ~ mass 1 x mass 2 distance 2 Or Of course, the gravitational attraction between the moon and Earth make them revolve around each other, but because we’re on the earth, we say that the moon orbits the earth. Actually, the moon “falls” toward the earth. It has just enough tangential speed to travel in a trajectory parallel to the earth’s surface. Moon orbit applet

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The Universal Gravitational Constant, G Remember the equation: Mathematically, when you have a “proportionality” equation like this, you can do experiments to find a “proportionality constant” that you can use to make the equation an exact equality. For gravity, experiments have shown that the exact equation is: Where G is called the Universal Gravitational Constant, and has the value: G = 6.67 x 10 -11 Nm 2 /kg 2 Physics Place Videos You can calculate your weight from this equation if you know Your mass The earth’s mass Your distance from the earth’s center of mass You should get the same answer as you do when you use “Weight = mg”

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The Inverse Square Law A law that has an equation with a “squared” term on the bottom is called an “inverse square law”. We’ll see other examples of this later in the course. Physics Place Videos The equation says that the force gets smaller very fast as you get farther away from the other object. This is because the force of attraction is spread out over a much bigger area as you get farther away. Physics Place Interactive Figure

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Question 1

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Question 2

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Weight and Weightlessness Physics Place Videos What if the chair is falling? Do you “feel” your weight? This is like you feel when you ride an elevator downward. Weightlessness is only a sensation; it is not a reality corresponding to an individual who has lost weight. As you are free-falling on a roller coaster ride (or other amusement park ride), you have not momentarily lost your weight. Weightlessness has very little to do with weight and mostly to do with the presence or absence of contact forces. The space shuttle is in orbit around the earth, so obviously it (and the astronauts on board) have “weight”. Yet, we always see and hear that they are experiencing “weightlessness”! The space shuttle is literally “falling around” the earth, so the astronauts don’t feel like they weigh anything.

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