Fundamental Physics I [Phys 131]                                  Fall 2004 Assignment #7 Reading, Objectives, & Problems A. Availability and Due Dates Assignment #7 is available Tuesday, November 9, 2004.  The target date for its successful completion is Thursday, November 18, 2004.  In any event, all of the Type A problems from Assignment #7 must be successfully completed and turned in by 5:00 pm on Friday, December 3, 2004.  If this requirement is not met, the student will not be allowed to take Quiz 4, to be given in class on Tuesday, December 7, 2004.   B. Reading As preparation for completing the problems in Assignment #7, read Chapters 14 & 15 in Cohen's The Fundamentals of College Physics, Volume IB. C. Objectives In addition to the Objectives listed on Assignments 1- 6, after completing Assignment #7, the student should [1] Be able to explain the difference between internal and external forces when these terms are used to refer to extended systems. [2] Realize that forces internal to an extended system are irrelevant as far as the bulk motion of the entire system is concerned.  The student should be able to explain why this is true. [3] Understand the terms rotation and translation, and realize that an extended body can experience each of these types of motion.  The student should also realize that this implies the existence of two distinct types of kinetic energy:  translational kinetic energy and rotational kinetic energy. [4] Be able to use Newton's Law and/or the Work-Energy theorem to analyze the motion of extended systems in arbitrary situations. [5] Understand what is meant by the terms rotational position, rotational velocity, rotational acceleration, torque, and rotational mass.  Know what the conventional symbol for each of these quantities is, and know the units in which each is measured. [6] Know that, for the various terms listed in Objective [5] above, the adjective "rotational" is often replace by the adjective "angular".  Know that this does not change the meaning of the terms. [7] Realize that every translational expression utilized in the class so far may be turned into a rotational expression simply by changing each translational variable into its rotational analogue.  Be able to carry out such equation transformations. [8] Know the specific relationships between all tangential variables and all rotational variables. [9] Understand and be able to explain the difference between rotational position and rotational displacement.   [10] Understand the definition of the unit radian.  Be able to convert back and forth between radians and degrees at will. [11] For an object that is rolling without slipping, understand the relationship between the translational velocity of the object and the rotational velocity of the object. [12] Know that the terms rotational mass and moment of inertia are used interchangeably.  Given sufficient information, be able to calculate the moment of inertia for a collection of point objects.  Realize that the moment of inertia of an object has meaning only after the axis of rotation has been given. [13] For simple shapes rotating about given axes, be able to predict the relative sizes of the moments of inertia of the various shapes. [14] Be able to determine the torque produced when a given force acts upon a system. [15] Be able to calculate the rotational kinetic energy of a system, given sufficient information. [16] Be able to incorporate the effects of massive pulleys into the solution of general dynamical problems. [17] Realize that, for an extended system in equilibrium, both the net force acting upon the system and the net torque acting upon the system are zero.  Be able to use this fact to analyze arbitrary extended systems that are in equilibrium. [18] Understand the term center of gravity, and be able to determine the location of the center of gravity of simple extended systems. D. Type A Problems [1] Do Problem 14.1 on p. 319 of Cohen. [2] Do Check Point 14.4 on p. 316 of Cohen. [3] A solid disc of mass 2 kg and radius 50 cm is originally rotating with an angular velocity of 18 rad/s.  A brake pad is then pressed against the outer rim of the disc.  As a result, the disc decelerates uniformly, ultimately coming to rest 20 seconds after the brake was first applied. Determine the total angle through which the disc turns while it is decelerating. Determine the torque caused by the brake. Determine the magnitude of the frictional force between the brake pad and the rim of the wheel. [4] A solid spherical ball rolls without slipping down a ramp that is declined at an angle of 30º from the horizontal.  After making it all of the way to the bottom of the ramp, the ball continues to roll along a horizontal surface.  If the length of the declined ramp is 140 cm, determine: The total kinetic energy that the ball has on the horizontal surface. (b) The rotational kinetic energy that the ball has on the horizontal surface. The speed of the ball on the horizontal surface. (d) Which of your answers to parts (a), (b), and (c) above would change if the ball were hollow instead of solid.  For each answer that would change, describe whether it would increase or decrease. [5] Do Problem 15.1 on p. 377 of Cohen. E. Type B Problems [6] Do Problem 15.2 on p. 378 of Cohen. [7] Do Check Point 15.1 on p. 323 of Cohen. [8] Do Check Point 15.14 on p. 350 of Cohen. [9] Do Check Point 15.22 on p. 365 of Cohen.