Circular Motion and Gravitation
3. A 1.10 x io3 kg object is dropped from a distance of 2.00 x io5 m onto the surface of
the moon. How fast is the object travelling when it hits the moon's surface?
kg)(i.io x io3 kg -- -—---2.ooxio5m+i.74xio m 1.74x10 m
= 6.67x10-
kg
-3.2O x io8 J
3.20 x io8 J
2
2
3.20 x io8 J = — (1.10 xio3 kg)(uf2) -- (i.ioxio3 kg)(o)
2
Vf
2
= 7.62 x io2 m/s
Practice Problems:
i.
What is the gravitational potential energy of a 5.00 x io3 kg satellite that is in an orbit
that has a radius of 9.90 x io6 m around the earth.
(Use gravitational potential energy = o at r = oo.)
(-2.0 x io11 J)
2. What is the work done against gravity on the satellite in the problem #1 in lifting it into
its orbit?
(l.ll x IO11 J)
3. What is the change in the gravitational potential energy of the satellite in problem #1 as
it is lifted from the earth's surface to its orbit?
(l.ll x IO11 J)
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What is the speed of a 1750 kg meteorite when it hits the surface of the moon? This
meteorite had a velocity of i.oo x io3 m/s heading directly toward the moon when it
was 15000 m above the moon's surface.
(1.02 x io3 m/s)
What is the gravitational potential energy of a 10.0 kg object when it is sitting on the
surface of the earth? (Use gravitational potential energy = o at r = oo.~)
(-6.25 x io8 J)
6.
What is the change in the gravitational potential energy of a 2.50 x io3 kg satellite as it
is lifted vertically into a circular orbit (radius = 6.90 x io6 m) around the earth?
(1.18 x io10 J)
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Circular Motion and Gravitation
LAUNCHING
PROBLEMS:
Formula:
v=
v=
Practice Problems:
l.
What is the escape speed at the moon's surface? (r = 1.74 x io6 m, M = 5.98 x 1024kg.)
(2.37 x io3 m/s)
2.
What is the escape speed at Jupiter's surface? (r = 7.18 x 10? m, mass = 1.9 x io2? kg)
(5.94 x io4 m/s)
3.
What is the mass of a planet that has an escape speed of 9.0 x io3 m/s and a radius of
7.2 x io6 m?
4.
What is the mass of a planet that has a radius of 2.57 x io6 m and an escape speed of
2.92 x io3 m/s?
(I.64xio 2 3kg)
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Circular Motion and Gravitation
Practice Problems:
i.
SUMMAR
Calculate the speed of the moon in its orbit around the earth.
(Radius of moon's orbit = 3.84 x io8 m moon's mass = 7.35 x io22 kg)
In this unit c
equations:
mu
r
(1.02 x io3 m/s)
2.
Calculate the speed of a satellite orbiting the earth at a height of 4.4 x IQS m above the
earth's surface. (Hint: remember to add the earth's radius of 6.38 x io6 m.)
(7.65 x io3 m/s)
3.
Calculate the orbital speed of a satellite 5.0 x io6 m above the surface of Jupiter,
(rj = 7.18 x 10? m, mj = 1.90 x lo2? kg)
equal to
This was de
force, i.e. th
used this wi
Again F
(4.06 x io4 m/s)
4.
Calculate the speed of earth in its orbit around the sun.
(Radius of earth's orbit = 1.50 x io11 m,ms = 1.98 x io3° kg)
(2.97 x io4 m/s)
5.
Using T = .
, calculate the time of one revolution (length of a year) on Mars.
(mM = 6.4 x io23 kg, ms = 2.0 x io3° kg, Radius of Mars' orbit = 2.3 x io11 m)
(6.0 x io7 s or 1.9 years)
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Circular Motion and Gravitation
Satellite.
Launching:
16. You find yourself on a planet where the potential energy of a 2.60 kg mass with respect
to the centre of the planet is 3.64 x io6 J. What is the escape velocity on this planet?
19. \
(1.91 x io3 m/s)
17. What is the mass of an a planet (radius = 5.85 x 10? m) which has an escape velocity of
2.54 x icH m/s?
2O.
JL
(2.83xl0 26 kg)
21.
18. What is the escape velocity on a planet that has a mass of 3.18 x io23 kg and a radius of
2.43 x io6 m?
(4.18xlO 3 m/s)
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Satellites in Orbit:
i respect
anet?
19. What is the speed of an artificial satellite (mass = 625 kg) which is placed in an orbit
i.oo x io6 m above the surface of a planet?(mp = 3.18 x io23 kg, rp = 2.43 x io6 m)
(2.49 x io3 m/s)
i x io3 m/s)
elocity of
20 < An artificial satellite (mass = 572 kg) is put into a circular orbit about the earth
(mass = 5.98 x io24 kg). If the radius of this orbit is 1.2 x io7 m, how long will it take to
make one revolution?
(1.3 x 1Q4 s)
2.83x10 kg)
i radius of
21. An artificial satellite (mass = 611 kg) is put into a circular orbit around Jupiter
(mass = 1.90 x lo2? kg, radius = 6.99 x 10? m). If this satellite has an orbital velocity of
3.12 x icH m/s, how far above Jupiter's surface is the satellite?
(6.03 x 10? m)
4.18xlO3 m/s)
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Circular Motion and Gravitation
Gravitational Potential Energy:
22. What is the gravitational potential energy of the moon with respect to the earth?
1.
(-7.63xio28J)
23. What is the change in the gravitational potential energy of a 10.0 kg object when it is
lifted vertically to a height of 6.38 x io6 m above the surface of the earth?
(3.13 x io8 J)
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