Universal Gravitation

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• Universal Gravitation
• Newton
• Cavendish
• Examples
• Whiteboards

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Newton Apple falls on his head? Newton knows
four things Distance apple is from the earths
center Distance it falls in a second Distance the
moon is from the earths center Distance it
falls in a second
1643-1727
He concludes there is an inverse square
relationship F ? 1/r2
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Newton His law of universal gravitation so
far F Gm1m2 r2
1643-1727
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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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)
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F Gm1m2 r2
r Center to center distance m1 One of the
masses m2 The other mass G 6.67 x 10-11
Nm2/kg2
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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Whiteboards Gravity 1 2 3 4
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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
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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
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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
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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
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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
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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 moons 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 ?
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2.9 x 106 m