Chapter 13
13.1
What must the separation be between a 5.2kg particle and a 2.4 kg particle for their
gravitation attraction have a magnitude of
2.3
×
10
−
12
N
?
Newton’s Law of Universal Gravitation states
F
=
G
M m
r
2
r
=
G
M m
F
=
6.67
×
10
−
11
⋅
5.2
kg
⋅
2.4
kg
2.3
×
10
−
12
=
19.02
m
13.3.
A mass M is split into two parts, m and Mm whar are then separated by a a certain
distance.
What ratio m/M maximizes the magnitude of the gravitational force between the parts?
This is an optimization problem.
Let’s find the m that maximizes F by taking the derivative of F
with respect to m and setting it equal to 0.
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 Spring '10
 jojo
 Mass, General Relativity, Gravitational constant, Mm r2 Mm

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