Physics 341: Homework Questions Due October 1

1
A horse is urged to pull a wagon. The horse refuses to try, citing Newton's third law as a defense: The pull of the horse on the wagon is equal but opposite to the pull of the wagon on the horse. "If I can never exert a greater force on the wagon than it exerts on me, how can I ever start the wagon moving?" asks the horse. How would you reply?

2
a) Estimate the orbital period of a particle travelling in a circular orbit just above the surface of the Earth. Do the same for a particle just above the surface of Mercury. Then do the same estimate for a particle just above the surface of a rock, whose radius equals 10 cm., and whose mass is 23 kg.
b) What is so striking about these results?
c) What reason can you give for this result?

3
A planet of mass M and a single satellite of mass M/10 revolve in circular orbits about their stationary center of mass, being held together by their gravitational attraction. The distance between their centers is D.
a) What is the period of this orbital motion?
b) What fraction of the total kinetic energy resides in the satellite?

4
The sun appears to be moving at a speed of about 250 km/sec in a circular orbit of radius about 25,000 light-years around the center of our galaxy. (One light-year is about 10**16 m.) The Earth takes 1 year to describe an almost circular orbit of radius about 1.5x10**11 m around the Sun. What do these facts imply about the total mass responsible for keeping the Sun in its orbit? Obtain this mass as a multiple of the sun's mass M. (Note that you do NOT need to introduce the numerical value of G to obtain your answer.)