Universal Gravitation

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Presentation transcript:

Universal Gravitation Newton Cavendish Examples Whiteboards

Newton: Apple falls on his head? Newton knows four things: Distance apple is from the earth’s center Distance it falls in a second Distance the moon is from the earth’s center Distance it “falls” in a second 1643-1727 He concludes there is an inverse square relationship: F  1/r2 TOC

Newton: r His law of universal gravitation so far: F = Gm1m2 r2 m2 m1 1643-1727 r m1 m2 What to use for G? r = Center to center distance m1 = One of the masses m2 = The other mass G = Universal gravitation constant TOC

Cavendish Determines the value of G in 1798 F = Gm1m2 r2 Measures F, both masses, and r G = 6.67 x 10-11 Nm2/kg2 (units cancel) TOC

r F = Gm1m2 r = Center to center distance r2 m1 = One of the masses m2 = The other mass G = 6.67 x 10-11 Nm2/kg2 r m1 m2 Example 1 - Find the force of gravity between a .756 kg stapler, and a .341 kg marker that is 1.75 m away? Example 2 - What is the force of gravity between a 1.0 kg mass, and the earth? (r = 6.38 x 106 m, mearth = 5.97 x 1024 kg) (check use of scientific notation) TOC

Whiteboards: Gravity 1 | 2 | 3 | 4 TOC

What is the force of gravity between a 5. 2 kg shot and a 250 What is the force of gravity between a 5.2 kg shot and a 250. kg wrecking ball whose centers are 2.45 m distant? F = Gm1m2 G = 6.67E-11 Nm2kg-2 r2 F = ?, m1 = 5.2 kg, m2 = 250. kg, r = 2.45 m W 1.44 x 10-8 N

Another shot is 1. 45 m from the center of a 250 Another shot is 1.45 m from the center of a 250. kg wrecking ball and experiences a force of 1.55 x 10-7 N, what is the mass of the shot? F = Gm1m2 G = 6.67E-11 Nm2kg-2 r2 F = 1.55E-7 N, m1 = ?, m2 = 250. kg, r = 1.45 m W 19.5 kg

What distance from the center of a 512 kg wrecking ball must a 4 What distance from the center of a 512 kg wrecking ball must a 4.5 kg bowling ball be to experience a force of 1.13 x 10-9 N? F = Gm1m2 G = 6.67E-11 Nm2kg-2 r2 F = 1.13E-9 N, m1 = 4.5 kg, m2 = 512 kg, r = ? W 11.7 m

The moon has a mass of 7. 36 x 1022 kg, and a radius of 1. 74 x 106 m The moon has a mass of 7.36 x 1022 kg, and a radius of 1.74 x 106 m. What does a 34.2 kg mass weight on the surface? F = Gm1m2 G = 6.67E-11 Nm2kg-2 r2 F = ?, m1 = 7.36E22 kg, m2 = 34.2 kg, r = 1.74E6 m W 55.5 N

The moon has a mass of 7. 36 x 1022 kg, and a radius of 1. 74 x 106 m The moon has a mass of 7.36 x 1022 kg, and a radius of 1.74 x 106 m. What mass weighs 25 N on its surface? F = Gm1m2 G = 6.67E-11 Nm2kg-2 r2 F = 25 N, m1 = 7.36E22 kg, m2 = ?, r = 1.74E6 m W 15 kg

The moon has a mass of 7. 36 x 1022 kg, and a radius of 1. 74 x 106 m The moon has a mass of 7.36 x 1022 kg, and a radius of 1.74 x 106 m. At what distance from the moon’s center would a 43 kg mass weigh 25 N? F = Gm1m2 G = 6.67E-11 Nm2kg-2 r2 F = 25 N, m1 = 7.36E22 kg, m2 = 43 kg, r = ? W 2.9 x 106 m