Problems on Newton's Law
Problem 2.1:
If a space shuttle is launched from the equator, what eastward speed
(relative to the ground) is required to propel it into a low-earth
orbit (
r re)? Take into account the rotation of the earth in
this problem.
[Solution]
Problem 2.2:
What if the space shuttle, instead of being launched from the equator,
is launched from Melbourne, Australia, at a latitude of 38
o
below the equator? Again, calculate the required eastwards speed.
[Solution]
Problem 2.3:
Calculate the value for
G which would be given by a Cavendish
apparatus (in an imaginary universe) set
up as shown:
and with
M = 5 kilograms,
m = 1 kilogram,
θ = 30 degrees,
and
r = 0.05 meters. Also, the
force exerted by the fiber is given by
F = 10-11sinθ.
[Solution]
Problem 2.4:
Calculate
g on the moon due to the moon's gravity. Compare this to the
gravitational force exerted on a mass
m on the moon due to the earth (ie. what
is g for the earth at the height of the moon?)(The mass of the moon is
Mm = 7.35×1022
and its radius
rm = 1700 kilometers, the earth-moon
distance is
r = 3.84×108 meters, the mass of the earth is
5.98×1024 kilograms).
[Solution]
Problem 2.5:
A ball is dropped from a height of 1000 kilometers above the earth. Calculate
the time taken for it to hit the ground as given by i) assuming
g takes the
value at the surface of the earth; ii) assuming
g takes the value at the top
of the ball's path. The mass of the earth is
5.98×1024 kilograms.
[Solution]
re)? Take into account the rotation of the earth in
this problem.
[Solution]
and with M = 5 kilograms, m = 1 kilogram, θ = 30 degrees,
and r = 0.05 meters. Also, the
force exerted by the fiber is given by F = 10-11sinθ.
[Solution]
