Newton’s Law of Universal Gravitation: Two objects of mass m1 and m2 separated by a center-to-center distance r ___________ each other with a gravitational force: attract r m1 m2 Fg Fg Fg = …where G = ____________________________ is called the _______________ gravitational constant.

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Newton’s Law of Universal Gravitation: Two objects of mass m1 and m2 separated by a center-to-center distance r ___________ each other with a gravitational force: attract r m1 Fg m2 Fg G m1 m2 r2 Fg = …where G = ____________________________ is called the _______________ gravitational constant.

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Newton’s Law of Universal Gravitation: Two objects of mass m1 and m2 separated by a center-to-center distance r ___________ each other with a gravitational force: attract r m1 Fg m2 Fg G m1 m2 r2 Fg = 6.67 x 10-11 N·m2/kg2 …where G = ____________________________ is called the _______________ gravitational constant. universal

Notes: Fg is an _________ range, _______________ force. Fg is stronger when the objects are__________ . 3. The constant G is very __________  Fg is the ________________ of the fundamental forces. 4. Fg is always ___________________. 5. Both masses pull each other with ____________ magnitude forces, but in _____________ directions. 6. Equation is only true for ____________ masses.  for spheres, you must assume mass is concentrated at __________________  for complicated shapes, _____________ is needed, but equation works ________________ anyway. infinite "at a distance" closer small weakest attractive equal opposite point its center. calculus approximately

Ex. A mass of 1.8 x 103 kg (F-150) is 0.50 meter from a mass of 6.0 x 101 kg (student). Find the magnitude of the force of gravitational attraction between the two masses. Show all work. G m1 m2 r2 Fg = (6.67 x 10-11 Nm2/kg2) (1.8 x 103 kg) (6.0 x 101 kg) Fg = (0.50 m)2 (7.2 x 10-6 Nm2) Fg = (0.25 m2) / Fg = 2.9 x 10-5 N ≈ 3/1000 of one dollar bill neither Which mass pulls with a greater force?

G m1 m2 r2 Fg = inverse squared Fg m1 Fg m2 Fg r direct direct Double m1  Fg ________________ Triple m2  Fg ________________ Double both m1 and m2  Fg ________________ Triple m1 and double m2 Fg ________________ Double r  Fg ________________ Halve r  Fg ________________ Triple r  Fg ________________ Double m1 and r  Fg ________________ Double m1, m2 and r  Fg ________________ 2x greater 3x greater 4x greater 6x greater 4x weaker 4x greater 9x weaker 2x weaker same

Ex: If the Fg is between an object of mass m and a planet, then Fg is called the _________: Fg = ___ weight w Ex: Earth m Fg = Gm1m2 r2 r = 1 Re GMem Fg = Re2 Me m GMe Fg = Re2 w = m g 1 Earth radius Re = ________________ Me = ________________ mass of Earth g = GMe/Re2 = 9.81 m/s2

Earth ms Ex: Are you weightless in the space shuttle (mass = ms)? The space shuttle orbits at ≈ _______ = __________ above Earth's surface. Its __________ distance from Earth's center is r = _____ + _____ Mm = _______ Mm. = ________ Re So the ___________ (Fg) of the shuttle and all its contents in orbit, compared to its weight on land, is: Earth Re = ___________ ≈ ___________ ms GMems GMems = Fg = = 

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Earth ms Ex: Are you weightless in the space shuttle (mass = ms)? The space shuttle orbits at ≈ _______ = __________ above Earth's surface. Its __________ distance from Earth's center is r = _____ + _____ Mm = _______ Mm. = ________ Re So the ___________ (Fg) of the shuttle and all its contents in orbit, compared to its weight on land, is: 300 km 0.3 Mm total Earth 6.4 0.3 6.7 1.05 6.37 x106 m weight Re = ___________ ≈ ___________ 6.4 Mm ms GMems GMems 0.91 GMems = Fg = = 91%  (1.05Re)2 (1.05)2 Re2 Re2

The Vomit Comet: The airplane produces about 25 s of apparent weightless-ness by following a parabolic vertical flight path. A parabolic flight path is the same path that would be taken by an object in free fall, such as a cannonball fired into the air.

Ex: r is the ____________________ distance center-to-center r = __ Re 4 C __ Re above surface 3 r = __ Re 3 B __ Re above surface 2 r = __ Re 2 A __ Re above surface 1 r = 1 Re Earth If Fg at surface = 200 N, what is the weight (Fg) at A? 200/22 = 200/4 = 50 N = 22 N At B? 200/32 At C? 200/42 = 12.5 N

Ex: A 20-N box on a table is lifted from 1 m to 2 m above the floor. Since the height was doubled, the new weight should be w = 20/22 = 5 N ?????? 5 N ? This _________ ______________ because these heights are from ________ _____________ . does not happen not measured 20 N 2 m Earth's table center 1 m

Ex: A 600-N volleyball player jumps in the air. What is the force of gravity acting on her… 1/ …while in the air? 2/ …as she is landing? 3/ …when she is again at rest on the ground? 4/ What is her weight in all three cases above? 600-N 600-N 600-N 600-N

Ex: A rock in Same rock at rest freefall: on a table: Fg = 1.33 N a/ What is the weight of the rock in each case? 1.33 N b/ What is the net force acting on the rock in each case? free fall: Fnet = ______ on table: Fnet = ______ -1.33 N c/ What is the acceleration of the rock in each case? free fall: a = ______ on table: a = ______ -9.81 m/s2 d/ What is the reaction force to the weight of the rock in each case? The rock pulls up on Earth with a 1.33 N gravitational force.

Ex: Cavendish "Weighing the Earth" Experiment: When a ____ sphere (m2) was brought close to the barbells, the _______________ attraction caused the thin wire to _________ . Pb thin wire From the wire's properties, the ______________ needed to make the wire twist that much could be _____________ gravitational force, Fg r m2 m1 Pb barbells twist estimated Then Fg, r, m2 and m1 were substituted into: G m1 m2 r2 Fg = and this was solved to find ______ . G G Once _____ was known, an object of known mass m and weight w were used to find ___________ unknown mass Me using G m Re2 Me w = Earth's

One last note: In PhysRT: g = Fg/m Solve this for: Fg = mg same ________ equation Not in PhysRT: w = mg acceleration ____________ due to gravity Even though g appears in the equation for w, an object does NOT have to be ________________ to use this equation. Think of g as simply a ________________________ between ____ and ____ . In fact, g can have ___________________ in different locations, which is why ____________ may change even though _________ remains the same. accelerating conversion factor m w different values weight mass