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# lecture10 - Gravitation Thursday, October 28, 2010 More...

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Unformatted text preview: Gravitation Thursday, October 28, 2010 More Newton... Thursday, October 28, 2010 Newton’s Law of Gravitation Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. Thursday, October 28, 2010 Newton’s Law of Gravitation For any two objects with mass m1 and m2, separated a distance r apart: m1 m2 Fg = G 2 r G = 6.674 × 10−11 N · m2 /kg 2 Gravitational Constant Thursday, October 28, 2010 Newton’s Law of Gravitation m1 m2 Fg = G 2 r Thursday, October 28, 2010 Treat Massive Objects As Point Objects* * Only if they are spherically symmetric Thursday, October 28, 2010 Earth’s Gravity Local Value of g at UCSB: 9.79624 m/s2 Thursday, October 28, 2010 Earth’s Gravity Fg,Earth mmE =G 2 r Where does g come from? Thursday, October 28, 2010 Calculating g w = mg Fg,Earth mmE =G 2 r mmE mg = G 2 r Thursday, October 28, 2010 Calculating g GmE g= 2 RE mE = 5.97 × 1024 kg RE = 6378 km Thursday, October 28, 2010 A Better Definition of Weight The weight of an object is the total gravitational force exerted on the object by all other objects in the universe. Thursday, October 28, 2010 Example... You’re involved in the design of a mission carrying humans to the surface of the planet Mars, which has a radius RMars = 3.38*106 m and a mass mMars = 6.42*1023 kg. The Earth weight of the Mars lander is 39,200 N. Calculate the weight Fg of the Mars lander and the acceleration due to Mars’ gravity, gMars. (a) at the surface of Mars, and (b) at 6.00*106 m above the surface of Mars (corresponding to the orbit of the Martian moon Phobos). Thursday, October 28, 2010 Weightlessness? Thursday, October 28, 2010 Satellite Motion Thursday, October 28, 2010 Satellite Motion Thursday, October 28, 2010 Uniform Circular Motion!?!@?!111 Thursday, October 28, 2010 Uniform Circular Motion! Thursday, October 28, 2010 Uniform Circular Motion! Fcentripetal v2 =m r ￿ Fg,Earth mmE =G 2 r v= GmE r Thursday, October 28, 2010 Example... At a given point above the surface of the earth, the gravitational acceleration is equal to 5.7 m/s2. The altitude of this point, above the surface of the earth, in km, is closest to: A) 2000 B) 2500 C) 3700 D) 5100 E) 6200 Thursday, October 28, 2010 Beyond Newton Thursday, October 28, 2010 Beyond Newton General Relativity Einstein 1907-1915 Thursday, October 28, 2010 Black Holes! Thursday, October 28, 2010 Black Holes! Schwarzschild Radius 2GM RS = c2 Thursday, October 28, 2010 Black Holes! Thursday, October 28, 2010 A person pushes on a stationary 125 N box with 75 N at 30° below the horizontal, as shown in the figure. The coefficient of static friction between the box and the horizontal floor is 0.80. From Mastering Physics... What is the normal force on the box? What is the friction force on the box? The person now replaces his push with a 75 N pull at 30° above the horizontal. Find the normal force on the box in this case. Thursday, October 28, 2010 Energy... Thursday, October 28, 2010 Conservation of Energy The total energy in any isolated system is constant, no matter what happens within the system. Energy can be converted from one form into another, but it cannot be created or destroyed. Thursday, October 28, 2010 Kinetic Energy Energy of Motion! Thursday, October 28, 2010 Potential Energy Thursday, October 28, 2010 Potential Energy Thursday, October 28, 2010 Potential Energy Thursday, October 28, 2010 ...
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## This note was uploaded on 01/17/2011 for the course PHYS 6a taught by Professor Stanek during the Fall '07 term at UCSB.

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lecture10 - Gravitation Thursday, October 28, 2010 More...

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