Physics 321 -- Spring 2003

Homework #9, due Wednesday April 2

1. (2) Marion & Thornton: problem 5-19. Hint: You need to calculate the rotational velocity of the Moon relative to the (moving) surface of the Earth.

2. (4) Marion & Thornton: problem 8-6. Hint: Use conservation of momentum and energy.

3. (4) Marion & Thornton, problem 8-10. Hint: Calculate the total energy of the Earth’s orbit (algebraically, not with numbers) both before and after the sun loses half its mass.

4. (5) Marion & Thornton, problem 8-9.

5. (6) Marion & Thornton, problem 8-5. Hint: First use F=ma to calculate the period of the circular orbit. (You can use the concept of reduced mass if you wish.) Then consider what happens after the particles are stopped. Write down an equation of motion for the particle separation x, using conservation of energy. Remember to use the reduced mass in the expression for kinetic energy. Then you need to integrate dt=dx/xdot to find the time until the particles collide. After a variable change x=y², the integral will be in the form of Eq. E-7 in Appendix E. Good luck!

6. (4) Marion & Thornton, problem 8-21. You can do this problem purely mathematically, or you can draw a clear diagram of several orbits passing through the same point with the same energy, and show that the circular orbit has the greatest angular momentum.