Download Wksht Review 1 formerly gravitational force

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Review 1 Planetary Motion
Gravitational Force – Worksheet
1. Calculating Gravitational Force:
a) A 70 kg student stands in the doorway:
i.
What is the gravitational force on the student from another 70 kg student who is
0.3 m (center-to-center) away?
ii.
What is the gravitational force on the student from the earth?
iii.
How much bigger is the value of the force of gravity from the earth compared to
the student? (Divide: Fg, earth/Fg, student)
2. “Change problems”
a) The force of gravity between two masses is 36 N, What will be the force if one mass is
doubled and the distance between them is tripled?
b) Mars has a radius 0.54 times that of the Earth and a mass 0.11 times that of the Earth.
If the force of gravity on your mass is 600 N on Earth, what will it be on Mars?
c) How does the centripetal acceleration change if you increase the speed by a factor of 4?
3. “Little g”
a) On the earth:
i.
Using the equation Fg=Gm1m2/r2 and Fg=mg*, show that g on the surface of the
earth is approximately 9.8 m/s2.
ii.
If one could throw a ball up in the air with an initial velocity of 20 m/s [up], what
would be the ball’s maximum height? how long would the ball be in the air?
b) On the moon
i.
Find g on the moon
ii.
If one could throw a ball up in the air with an initial velocity of 20 m/s [up], what
would be the ball’s maximum height? how long would the ball be in the air?
4. Finding the mass of a planetary of stellar body
a) An astronomer observes the planet Jupiter and finds that the period of its moon is
1.5x105 s. If this moon has an average radius of orbit about Jupiter of 4.2 x 108m. What
is the mass of Jupiter, using these measurements?
b) Communications satellites are place in orbit so that they remain stationary relative to a
specific area on the Earth’s surface. They are given the name synchronous satellites
because, to maintain such a position, their period as they orbit must be the same as the
Earth’s. What is the height of such a satellite measured from i)the center of the earth?
ii) the surface of the earth? How fast will the satellite be travelling in its orbit?
R3
is known as the “Kepler constant”, and is known to be a constant for all
T2
R3
objects orbiting the same object. Starting with the equation: Fc=Fg , solve for 2 in
T
c) The term
terms of the mass of the planet being orbited (hint: use the substitution v 
2R
in the
T
equation)
d) Use the results of c to calculate the mass of the sun from the radius and period of the
earth’s orbit. (use 1.5 x 1011 m for the radius of the Earth’s orbit)
5. Name one object that has the same value of
R3
as
T2
a) the Earth
b) the Moon
answers: 1ai) 3.63x10-6 N, ii) 686N, iii) 1.89x108 , 2a) 8N, b) 226N, c) increase by a factor
of 16. 3a ii) 20.4 m, b i) 1.62 m/s2, ii) 125m, 4a) 1.95x1027kg, b) i) 4.23x107m,
ii)3.59x107m, c) ask, d) 2x1030 kg, 5. ask