PHYS 2101

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PHYS 2101
Fall 2009

• Gravitational Potential Energy
• Escape Speed
• Keplers Third Law

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PHYS 2101
Fall 2009
Two blocks are connected by a string over a
pulley with mass mp. (m1 gt m2) Derive an
expression for the magnitude of the acceleration
of the blocks, in terms of g and the three
masses. Treat the pulley as a uniform disk.
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PHYS 2101
Fall 2009
Two blocks are connected by a string over a
pulley with mass mp. (m1 gt m2) Derive an
expression for the magnitude of the acceleration
of the blocks, in terms of g and the three
masses. Treat the pulley as a uniform disk.
for disk
no slip condition
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PHYS 2101
Fall 2009
CT1
Two particles lie along the x-axis separated by a
distance 2d, as shown below. The particle on the
left has a mass of 2m and the particle on the
right has a mass of 3m. At which point on the
axis will the gravitational potential energy on a
third particle with mass m be the least? 1 -
A 2 - B 3 - C
A
B
C
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PHYS 2101
Fall 2009
EX1
Calculate the gravitational potential energy on a
third particle with mass m at each point? 1 -
A 2 - B 3 - C
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PHYS 2101
Fall 2009
CT2
Two particles lie along the x-axis separated by a
distance 2d, as shown below. The particle on the
left has a mass of 2m and the particle on the
right has a mass of 3m. At which point on the
axis should you add a third particle with mass m
so that the gravitational potential energy of the
system of particles will be the lowest? 1 -
A 2 - B 3 - C
A
B
C
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PHYS 2101
Fall 2009
EX2
Calculate the gravitational potential energy of
the system if a particle of mass m is placed at
each point? 1 - A 2 - B 3 - C
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PHYS 2101
Fall 2009
CT3
Rank the four arrangements shown below according
to the gravitational potential energy of the
particle labeled m, from greatest to least.
2
1
3
4
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PHYS 2101
Fall 2009
CT4
Rank the four arrangements shown below according
to the gravitational potential energy of the
system of particles, from greatest to least.
2
1
3
4
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PHYS 2101
Fall 2009
EX3
A rocket is launched vertically upward at 3.1
km/s. How high does it go?
A ball is thrown vertically upward at 3.1 m/s.
How high does it go?
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PHYS 2101
Fall 2009
EX4
In leaving the solar system, Voyager 1 used
Saturn as a slingshot to attain its escape speed.
What speed did Voyager 1 need to reach to escape
the solar system?
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PHYS 2101
Fall 2009
EX5
A satellite is placed in an elliptical orbit
around the Earth. At perigee (the point of
closest approach), the satellite is 2.00x106 m
away. At apogee (the point of greatest
distance), the satellite is 1.87x107 m away. If
the speed of the satellite is 8450 m/s at
perigee, how fast is it traveling at apogee?
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PHYS 2101
Fall 2009
A satellite that is in low Earth orbit moves to a
higher orbit while keeping its total mechanical
energy constant. (b) What happens to the
kinetic energy of the satellite? 1 - increase 2
- decrease 3 - stay the same
A satellite that is in low Earth orbit moves to a
higher orbit while keeping its total mechanical
energy constant. (c) What happens to the speed
of the satellite? 1 - increase 2 - decrease
3 - stay the same
CT5
A satellite that is in low Earth orbit moves to a
higher orbit while keeping its total mechanical
energy constant. (a) What happens to the
potential energy of the satellite? 1 -
increase 2 - decrease 3 - stay the same
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PHYS 2101
Fall 2009
EX6
If the mean distance from the sun to the Earth is
1.50x1011 m, what is the mass of the sun?
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PHYS 2101
Fall 2009
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PHYS 2101
Fall 2009
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PHYS 2101
Fall 2009
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PHYS 2101
Fall 2009
EX7
S2 orbits Sagittarius A with a period of T
15.2 y (4.79 x 108 s) along an orbit with a
semimajor axis of a 5.50 light-days (1.42 x
1014 m). What is the mass of Sagittarius A?