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382
Universal Gravitation
Q13.7
Ten terms are needed in the potential energy:
U
UUUUUUUUUU
=+++++++++
12
13
14
15
23
24
25
34
35
45
.
With
N
particles, you need
i
NN
i
N
−=
−
=
∑
1
2
1
2
a
f
terms.
Q13.8
No, the escape speed does not depend on the mass of the rocket. If a rocket is launched at escape
speed, then the total energy of the rocketEarth system will be zero. When the separation distance
becomes infinite
U
=
0
af
the rocket will stop
K
=
0
. In the expression
1
2
0
2
mv
GM m
r
E
, the mass
m
of the rocket divides out.
Q13.9
It takes 100 times more energy for the 10
5
kg spacecraft to reach the moon than the 10
3
kg
spacecraft. Ideally, each spacecraft can reach the moon with zero velocity, so the only term that need
be analyzed is the change in gravitational potential energy.
U
is proportional to the mass of the
spacecraft.
Q13.10
The escape speed from the Earth is 11.2 km/s and that from the Moon is 2.3 km/s, smaller by a factor
of 5. The energy required—and fuel—would be proportional to
v
2
, or 25 times more fuel is required
to leave the Earth versus leaving the Moon.
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .
 Fall '11
 Staff
 Physics, Energy, Potential Energy

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