Problems for Newton's Law
Problem 1.1:
What is the force exerted by Big Ben on the Empire State building? Assume that
Big Ben has a mass of
108 kilograms and the Empire State building
109
kilograms. The distance between them is about 5000 kilometers and Big Ben is
due east of the Empire State building.
[Solution]
Problem 1.2:
What is the gravitational force that the sun exerts on the earth? The
earth on
the sun? In what direction do these act? (
Me = 5.98×1024 and
Ms = 1.99×1030
and the earth-sun distance is
150×109 meters).
[Solution]
Problem 1.3:
Figure E.1: alignment of Mercury, Venus and the Sun.
If Mercury, Venus and the sun are aligned in a right triangle, as shown, then
calculate the vector sum of the
forces on Venus due to both Mercury and the Sun. What is the direction and
magnitude of the resulting
force? (Sun-Venus distance
rv = 108×109 meters, Sun-Mercury distance
rm = 57.6×109 meters, mass of Sun
Ms = 1.99×1030 kilograms, mass of Mercury
Mm = 3.3×1023 kilograms, mass of Venus
Mv = 4.87×1024 kilograms).
[Solution]
Problem 1.4:
It is possible to simulate "weightless" conditions by flying a plane in an arc
such that the centripetal acceleration exactly cancels the acceleration due to
gravity. Such a plane was used by NASA when training astronauts. What would be
the required speed at the top of an arc of radius 1000 metres?
[Solution]
Problem 1.5:
Show using Newton's Universal Law of Gravitation that the period of orbit of
a binary star system is given by:
Where
m1 and
m2 are the masses of the respective stars and
d is the
distance between them. Notice that we derived the same result in a problem in
the previous section, using the reduced mass and Kepler's Third Law.
[Solution]
If Mercury, Venus and the sun are aligned in a right triangle, as shown, then
calculate the vector sum of the
forces on Venus due to both Mercury and the Sun. What is the direction and
magnitude of the resulting
force? (Sun-Venus distance rv = 108×109 meters, Sun-Mercury distance
rm = 57.6×109 meters, mass of Sun Ms = 1.99×1030 kilograms, mass of Mercury
Mm = 3.3×1023 kilograms, mass of Venus Mv = 4.87×1024 kilograms).
[Solution]
