1. Universal Gravitation
Newton
Cavendish
Examples
Whiteboards

2. 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
He concludes there is an inverse square relationship:
F  1/r2
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3. Newton: r His law of universal gravitation so far: F = Gm1m2 r2 m2 m1 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
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4. Cavendish Determines the value of G in 1798 F = Gm1m2 r2
Measures F, both masses, and r
G = 6.67 x Nm2/kg2
(units cancel)
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5. r F = Gm1m2 r = Center to center distance r2 m1 = One of the masses
m2 = The other mass
G = 6.67 x 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)
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6. Whiteboards:
Gravity
1 | 2 | 3 | 4
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7. 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

8. 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

9. 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

10. 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

11. 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

12. 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