Gravitation

1) If someone were so unfortunate as
to step into a hole bored from one side of the earth to the other, what would
be their motion through the tunnel? Neglect air resistance.

2) If air resistance were a factor in
Question 1, how would the person’s motion change?

3) The weight of an apple near the
surface of the earth is about 1 N. What is the weight of the earth in the
gravitational field of the apple? Which of

4) Suppose that for some odd reason
you have sealed yourself inside a windowless box. After a while you notice that
objects no longer fall to the floor when released from your hand. Without
reference to anything outside the box, how can you tell whether you and the box
are in free fall or gravity has been mysteriously turned off?

5) The mass of the earth is 5.97 ´ 10^{24} kg, and
its radius is 6370 km. A TV satellite with a 200 kg mass is in a circular orbit
of radius 40,000 km around the center of the earth. Find the gravitational
force on the satellite. Next, calculate the weight of the satellite if it were
on Earth instead of in orbit, and find the percentage decrease when it’s in
space.

6) In the late 1700’s, a clever person
by the name of Henry Cavendish calculated the mass of the Earth. To do so, he
first had to measure the gravitational constant, G. He found that a sphere of
mass 0.8 kg attracted another sphere of mass 0.004 kg with a force of 1.3 ´ 10^{-}^{10} N when the distance
between the centers of the spheres was 0.04 m. The acceleration due to gravity
was already known to be 9.8 m/s^{2} and the radius of the planet had
been measured as 6400 km. First, calculate G. Second, find the mass of Earth.
Use only this data.

7) Imagine three masses at the angles
of an isosceles triangle. The base of the triangle is 0.16 m long, and each of
the upright legs is 0.10 m. The masses at the two angles on the base are each
6.4 kg, and the mass at the peak of the triangle is 0.01 kg. If the only forces
acting on the 0.01 kg mass are the attractions from the 6.4 kg masses, find the
initial direction and magnitude of the acceleration of the 0.01 kg mass at the
instant it is released.