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Transcript
Chapter 2 completion... Thursday, January 31 Spring 2008 Momentum • • • • Motion depends on mass and speed Linear momentum: p = mv Law of conservation of linear momentum Angular momentum – the right-hand rule Universal Gravitation “...the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from earth, but that this power must extend much further than was usually thought. Why not as high as the Moon...?” Newton’s illustration from Mathematical Principles of Natural Philosophy Launching Into Orbit Universal Gravitation F= Gm1m2 d2 The universal gravitational constant: G = 6.67 × 10-11 N·m2/kg2 The gravitational force between two objects is proportional to the mass (m) of each object and inversely proportional to the square of the distance (d) between the centers of the masses: The direction of the force is attractive and lies along the line joining the centers of the two masses. Universal Gravitation Gm1m2 F= d2 Newton’s law of universal gravitation obeys his 3rd law of motion: d F1 = F2 = F Universal Gravitation • The gravitational force between two objects is exerted by each object on the other (ME) (mass) • It demonstrates a 3rd law action-reaction pair of forces RE F= Gm1m2 d2 • The two objects may react differently, depending on their masses and the size of the force Weight and Gravity • Weight – Force of gravity acting on an object’s mass: W = mg • Weight depends on acceleration due to gravity (g = 9.8 m/s2 on Earth) – Different on Earth, Moon, Mars, etc. • Mass is constant – Amount of matter comprising an object – Independent of location in universe Mass and Weight Mass is a measure of the amount of matter in an object, and it determines an object’s inertia, or resistance to a change in its motion. The gravitational force acting on an object is the weight of the object. W = mg 1 N ≈ 0.225 lb; 1 lb ≈ 4.448 N Big G and Little g • Closely related: Force of Earth’s gravity on a mass at its surface: F = (G × mass × ME) / RE2 F = mass × g • Setting equations equal: mass × g = (G × mass × ME) / RE2 • Divide by mass g = (G × ME) / RE2 • Plug in values of g and G 9.8 m/s2 = 9.8 N·kg For Tuesday 02/05: Complete HW #2, Chapter 2 Mallard quiz (due by midnight on Monday 02/04) In-class quiz on Chapter 2