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# Lec9 - Today Chapter 9(Gravity Chapter 9 Gravity Newton...

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Today: -- Chapter 9 (Gravity)

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Chapter 9: Gravity Newton: made revolutionary connection between the circular motion of celestial bodies and the downward falling of objects on the earth: It is the one and the same gravitational force responsible for both the apple falling from the tree and the moon orbiting around the earth!
The universal law of gravity (Newton) Every mass m 1 attracts every other mass m 2 with a force: F ~ m 1 m 2 d 2 distance between their centers The greater (either of) the masses, the greater is the attractive force. The closer they are to each other, the greater the force – with an inverse-square dependence. The constant of proportionality is called the universal gravitational constant, G = 6.67 x 10 -11 N . m 2 /kg 2 = 0.0000000000667 N m 2 /kg 2 F = G m 1 m 2 d 2 Tiny! So gravitational forces between everyday masses at everyday distances (eg you and me) is negligible.

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Clicker Question If there was no earth (and no other planets/sun…), the moon would continue going in a straight line as shown by the solid arrow. The gravitational pull of the Earth draws the moon closer to it, hence it falls in an orbit around the earth, rather than directly into it. What would happen if the tangential speed of the moon was instead zero? A) It would still continue orbitting the Earth B) It would be stationary with respect to the Earth. C) It would fall straight down into the Earth….crash! D) None of the above Answer: C, due to the gravitational force of the Earth on the moon
Distance-dependence of gravity Inverse-square law: F ~ 1/d 2 Compare with paint-spray burst out from a can: the thickness of the paint varies in the same inverse-square way i.e. if 1-layer thick at 1m, then is ¼ layers thick at 2 m etc.

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Notes (1) d = distance between the center of masses of the objects. So when one of the objects is earth, then the relevant distance d = radius of the earth + distance of other object from earth’s surface. Distance-dependence continued…
Questions (1) What is the force of earth’s gravity on a 1-kg object at the surface of the earth? What do we commonly call this force? (2) If you climbed to the top of Mount Everest (height 8850 m), how much less would you weigh? Assume you eat on the way so that your mass remains fixed.

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When at rest on the launching pad, the force of gravity on the space shuttle is quite huge—the weight of the shuttle. When in orbit, some 200 km above Earth’s surface, the force of gravity on the shuttle is 1. nearly as much. 2. about half as much. 3. nearly zero (micro-gravity). 4. zero. (Neglect changes in the weight of the fuel  carried by the shuttle.) Clicker Question
1 . nearly as m uch. 2. about half as much. 3. nearly zero (micro-gravity). 4. zero. (Neglect changes in the weight of  the fuel carried by the shuttle.) When at rest on the launching pad,  the force of gravity on the space  shuttle is quite huge—the weight of  the shuttle. When in orbit, some  200 km above Earth’s surface, the  force of gravity on the shuttle is

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