Physics 321 -- Spring 2004

Homework #11, due at beginning of class Wednesday April 28.

1.         [6pts] Solve for the motion of the system described in problem 7-6 of Marion & Thornton WITHOUT using the Lagrangian method. The "inclined plane" is a triangular wedge that slides without friction on a horizonal surface. There are two coordinates in this problem -- a convenient choice is the horizontal coordinate of the wedge and the coordinate of the contact point of the hoop measured along the wedge. You may use energy and momentum conservation. Don’t forget that the hoop has both rotational and translational kinetic energy: its moment of inertia is I=mR².

2.         [6pts] Solve for the motion of the system described in problem 7-6 of Marion & Thornton using the Lagrangian method. This should be easier than the previous problem -- especially since in solving that problem you have already calculated the kinetic energy and the potential energy.

3.         [6pts] Marion & Thornton, problem 7-3. The motion is in the plane in which the cylinder is curved. The constraint of no slipping gives you a relationship between the angle that describes the center of the ball and the angle that describes its rotation. Note that the distance from the center of the sphere to the center of the hollow cylinder is R-rho.

4.         [6pts] Marion & Thornton, problem 7-12. Use the Lagrangian method: it would be much harder to use Newton's laws directly!

5.         [4pts] Marion & Thornton, problem 7-15.