Download (Honors Physics) Universal Law of Gravitation

Thompkins: PHYSICS: Universal Law of Gravitation
1. Find the force of gravity between two physics students that have masses of 74.0 kg
and 82.5 kg if they are sitting 95.0 cm apart.
2.
A 1450 kg spacecraft is drifting in space. The force of gravity between it and the
Earth is 3860 N.
a)
b)
How far is it from the center of the Earth?
How far is it above the surface of the Earth? (Earth radius = 6.38x106m)
3.
What would happen to the force of gravity on the spacecraft in question #2 if the
distance between the spacecraft and the center of the Earth was:
a)
Tripled?
b)
Halved?
4.
What is the force of gravity on a 24.0 kg table sitting on the Earth?
5.
6.
If the weight of a classroom Physics textbook is 42 N, what is the books mass?
If the textbook in question #5 was taken to the Moon, would its mass and/or weight
change?
Complete the following table for these objects
“g” is the force of gravity per kilogram (N/kg)
Weight is the force of gravity (N) and can be found by F=mg
7.
Object
Mass (kg)
Radius (m)
Moon
7.36x1022
1.74x106
Venus
4.87x1024
6.05x106
Earth
5.98x1024
6.38x106
Mars
6.40x1023
3.40x106
Jupiter
1.90x1027
7.15x107
Sun
1.99x1030
6.96x108
Gravitational
Field Strength “g”
at the surface of
the object (N/kg)
Weight of an 80.0 kg
student standing on
this object (N)
8.
What is the Earth’s gravitational field strength “g” at the top of Mt. Everest, which is
8400 m above sea level?
9.
What is the size of the force of gravity between the Earth and the Sun? A distance of
1.50x1011 m separates them.
10-11. Derive Kepler’s 3rd Law
12) A man takes his dog for a walk on a deserted beach. Treating people and
dogs as point objects for the moment, find the force of gravity between the 105
kg mand and his 11.2 kg dog when they are separated by a distance of (a) 1.00
m and (b) 10.0 m.
13) If you climb to the top of Mt. Everest, you will be about 5.50 mi above sea
level. What is the acceleration due to gravity at this altitude?
(a) Find the acceleration of gravity on the surface of the Moon.
(b) The lunar rover had a mass of 225 kg. What was its weight on the Earth and
on the Moon? (Mass of Moon
and its radius is
)
14) Find the mass of Mars, given that its radius is
acceleration of gravity on its surface is
, and that the
.
15) Find the altitude above the Earth's surface where a satellite orbits with a
period of one day
(
,
,
)
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16) The Earth revolves around the Sun once a year at an average distance of
. (a) Use this information to calculate the mass of the Sun. (b)
Find the period of revolution for the planet Mercury, whose average distance
from the Sun is
.
17)
A spacecraft of mass 1,000 kilograms is in an elliptical orbit about the Earth, as
shown above. At point A the spacecraft is at a distance rA = 1.2 x 107 meters from
the center of the Earth and its velocity, of magnitude VA = 7.1 x 103 meters per
second, is perpendicular to the line connecting the center of the Earth to the
spacecraft. The mass and radius of the Earth are ME = 6.0 X 1024 kilograms and rE =
6.4 X 106 meters, respectively.
Determine each of the following for the spacecraft when it is at point A .
a. The total mechanical energy of the spacecraft, assuming that the
gravitational potential energy is zero at an infinite distance from the Earth.
b. The magnitude of the angular momentum of the spacecraft about the center of
the Earth.
Later the spacecraft is at point B on the exact opposite side of the orbit at a
distance rB = 3.6 X 107 meters from the center of the Earth.
c. Determine the speed vB of the spacecraft at point B.
Suppose that a different spacecraft is at point A, a distance rA = 1.2 X 107 meters
from the center of the Earth. Determine each of the following.
d. The speed of the spacecraft if it is in a circular orbit around the Earth
e. The minimum speed of the spacecraft at point A if it is to escape completely
from the Earth