PHYSICS 218 Final Exam Fall, 2006 STEPS __________________________________________________________________ No calculators are allowed in the test. Be sure to put a box around your final answers and clearly indicate your work to your grader. All work must be shown to get credit for the answer marked. If the answer marked does not obviously follow from the shown work, even if the answer is correct, you will not get credit for the answer. Clearly erase any unwanted marks. No credit will be given if we can’t figure out which answer you are choosing, or which answer you want us to consider. Partial credit can be given only if your work is clearly explained and labeled. Partial credit will be given if you explain which law you use for solving the problem. Put your initials here after reading the above instructions: Do not fill out the information below until instructed to do so! Name:______________________ Signature:____________________ Student ID:__________________ ______________________ Section Number: _____________ For grader use only: Problem 1 (20) ___________ Problem 2 (20) ___________ Problem 3 (10) ___________ Problem 4 (20)___________ Problem 5 (15) ___________ Problem 6 (20)___________ Total (105) ___________

Problem 1: (20 points) Two blocks, with masses and, are stacked as shown and placed on a frictionless horizontal surface. There is friction (coefficient of friction ) between the two blocks. An external force is applied to the top block at an angle below the horizontal. a) Draw a free body diagram for each of these blocks. b) What is the maximum force F that can be applied for the two blocks move together. F x y

Problem 2: (20 points) A spring with negligible mass exerts a restoring force, if it is stretched or compressed ( and are known constants). A block of mass m is pushed against the spring so that the spring is compressed by amount of A. When the block is released, it moves along a frictionless, horizontal surface and then up the incline that has coefficient of friction. 1)Find the potential energy of the system before the block is released. 2)How far does the block travel up the incline before starting to slide back down? 1 2 mg N

Problem 3: (10 points) where An object of mass m is at rest in equilibrium at the origin. At t=0 a new forceis applied that has components are known constants. Calculate the velocity vector as a function of time.

Problem 4: (20 points) R A B H A car in an amusement park rides without friction around the track. It starts with velocity V 0 at point A at height H. 1)Find the velocity of the car at point B. Denote it as. 2)What is the radius R that the car moves around the loop without falling off. 2) To find the maximum radius, we need to find the magnitude of critical velocity for the car not to fall off the track. From the second law at point C: C From conservation of mechanical energy at points A and C: 1) Conservation of energy:

Problem 5: (15 points) Two masses, and, are attached by a massless, unstretchable string which passes over a pulley with radius R and moment of inertia about its axis I. The horizontal surface is frictionless. The rope is assumed NOT to slip as the pulley turns. Find the acceleration of mass. y x

Problem 6: (20 points) A bullet of mass m is fired with velocity of magnitude into a block of mass M. The block is connected to a spring constant k and rests on a frictionless surface. Find the velocity of the block as a function of time. (Assume the bullet comes to rest infinitely quickly in the block, i.e. during the collision the spring doesn’t get compressed.) k M x