1.
The
SunÕs gravitational pull on the Earth is much larger than the MoonÕs. Yet, the MoonÕs gravitational pull is
mainly responsible for the tides.
Can you explain this?

2.
The
Sun is directly below us at midnight, in line with the EarthÕs center. Are we then heavier at midnight, due to
the SunÕs gravitational force on us, than we are at noon? Make an estimate of the difference in
weight (if any).

3.
Consider
the system shown below. The
coefficient of kinetic friction between block A (with weight W_{a}) and
the table top is m_{k}.
(a) Calculate the weight W_{b} of the hanging block required if
this block is to descend at constant speed once it has been set into
motion. (b) Suppose the
coefficient of static friction is m_{s} = 0.4 and the mass of A
is 30 kg and the mass of B is 2 kg.
What is the force of friction on mass A now (assuming an initial
condition of no motion)? How will
the system move as time increases?

4.
The
density of a certain planet varies with radial distance as r(r) = r_{0}(1-ar/R_{0}) where R_{0} is the radius of
the planet, r_{0} is its central density,
and a is a dimensionless constant. (a) What is the total mass of the
planet? (b) Calculate the weight
of a one-kilogram mass located on the surface of the planet.

5.
The Earth
moves faster in its orbit around the sun in December than in June. Is it closer to the Sun in June or in
December? Does this effect the
seasons? Explain.

6.
Consider
the drawing below. In terms
of M_{1}, M_{2} and g, find the acceleration of each block in
the system. Assume there is no
friction anywhere in the system.
Check your solution with limiting cases.