1. Consider the pulley system to the right. The masses M and 3 M are simply hanging, while the mass 2 M is sitting on an inclined plane with coefficients of friction μs and μk .
a) Obtain an expression for the coefficient of static friction required to ensure the masses do not accelerate, which depends on the angle of the inclined surface.
b) Obtain an expression for the coefficient of kinetic friction required to ensure the masses move at a constant velocity when they do move, which depends on the angle of the inclined surface.
2. A bullet of mass m and initial velocity v0 passes through a block of mass M suspended by an unstretchable, massless string of length L from an overhead support. It emerges from the collision on the far side traveling at v1 < v0. This happens extremely quickly (before the block has time to swing up) and the mass of the block is unchanged by the passage of the bullet (the mass removed making the hole is negligible, in other words). After the collision, the block swings up to a maximum angle θmax and then stops. Find θmax.
3. In the figure above, a spool or pulley with moment of inertia βMR2 is hanging from a ceiling by a (massless, unstretchable) string that is wrapped around it at a radius R, while a block of equal mass M is hung on a second string that is wrapped around it at a radius r as shown. Find the magnitude of the acceleration of the the central pulley.
4. Write 5 multiple-choice exam questions on any topics of your choice. A good question should be of sufficient difficulty and perhaps have a good background story? Try to change questions you've seen previously? Post your favorite question to the blackboard discussion board!