Fundamental Physics I [Phys 131]            Fall 2004 Assignment #8 Reading, Objectives, & Problems A. Availability and Due Dates Assignment #8 is available Tuesday, November 16, 2004.  The target date for its successful completion is Tuesday, November 30, 2004.  In any event, all of the Type A problems from Assignment #8 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 16 and 17 in Cohen's The Fundamentals of College Physics, Volume IB. C. Objectives In addition to the Objectives listed on Assignments 1- 7, after completing Assignment #8, the student should [1] Realize that kinetic energy is conserved in a collision between two objects only when the displacement of each (entire) object is the same.  Realize also why this is true. [2] Know that collisions in which kinetic energy is conserved are referred to as elastic collisions.  The student should also recognize the term inelastic, which clearly refers to any collision that is not elastic. [3] Know the definition of linear momentum, know the standard symbol for linear momentum, and be able to calculate the linear momentum of an object or system of objects given sufficient information. [4] Know that total linear momentum of any system is conserved as long as there is no net external force acting on the system.  The student should also be able to explain the key difference between linear momentum and kinetic energy that forces the former to be conserved, while allowing the latter to be violated. [5] Be able to analyze arbitrary elastic collisions by conserving kinetic energy and linear momentum.  The student should be able to do this for collisions taking place in multiple dimensions as well as for one-dimensional collisions. [6] Be able to analyze arbitrary inelastic collisions by conserving momentum if sufficient additional information is provided.  Realize that any such collision within a system will induce a reduction in the total kinetic energy of the system. [7] Understand the definition of the term angular momentum.  Realize that the total angular momentum of any system is conserved as long as there is no net external torque acting on the system. [8] Be able to use conservation of angular momentum to analyze arbitrary problems involving rotating objects. [9] Know that, for each of the three conservation laws studied in Physics 131: (i) Conservation of Total Energy, (ii) Conservation of Linear Momentum, and (iii) Conservation of Angular Momentum, there is an associated symmetry of nature.  Realize further that any time there is a symmetry of nature, it implies the existence of an associated conservation law. [10] Know what is meant by the term Impulse.  Realize that the impulse applied to any system is equal to the change in momentum of that system. [11] Be able to explain qualitatively how energy is stored in the following forms:  Heat, Light, Sound, Chemical Bonds. [12] Know the definition of Power, and know that the SI unit in which power is measured is the Watt, shorthand for J/s.   D. Type A Problems [1] Do Problem 16.1 on p. 408 of Cohen. [2] An object with mass 5 kg is sliding from left to right along a frictionless surface with speed 10 m/s.  This object then collides head-on with a second object.  The second object has mass 10 kg, and is initially at rest before the collision. Determine the total momentum and total kinetic energy of the two objects before the collision. Assuming that the collision is elastic, determine the final speeds of both objects. Assume now that the collision is inelastic.  In particular, assume that precisely 100 Joules of kinetic energy are lost to heat during the collision.  Determine the final speeds of both objects. [3] Suppose now that the same two objects as in Problem [2] above collide, but that the impact is not precisely head-on.  As a result, the 10 kg object moves off at speed 4 m/s in a direction 30 degrees below the horizontal after the collision.  The 5 kg object moves off at speed v in a direction è above the horizontal after the collision.  Determine the values of v and è. [4] A child of mass 50 kg stands on the outer edge of a merry-go-round.  The merry-go-round may be modeled as a solid disc with mass 150 kg. and radius 3 meters.  Initially, the merry-go-round is spinning with angular velocity ù = 2 rad/s about an axis passing through its center. Determine the moments of inertia of the merry-go-round, IMGR , and the child, Ichild , about the axis of rotation. Add IMGR and Ichild to get the total moment of inertia of the system, ITOT . Determine the total angular momentum of the spinning system, L. Determine the total kinetic energy of the spinning system, KE. Now suppose that the child pulls himself all of the way in to the center of the merry-go-round. With what angular velocity is the merry-go-round now spinning? What is the total kinetic energy of the spinning system now? Your answer to part (f) should be greater than your answer to part (d).  Where did the extra energy come from? [5] A bicyclist of mass 90 kg sits upon a bicycle of mass 10 kg that is initially at rest.  The bicyclist then stomps on the pedals, and manages to accelerate to a speed of 10 m/s in 7 seconds.  Assuming that the road on which the cyclist rides is flat and ignoring air resistance, determine the average power produced by the cyclist during those first 7 seconds. E. Type B Problems [6] When two objects collide, the total momentum of the two objects immediately after the collision must be the same as that immediately prior to the collision.  The total kinetic energy of the two objects, however, may change during the collision.  Explain the origin of this difference. [7] An unfortunate bridge design is shown below.  Among other problems, the two top sections of the bridge have been left simply resting on their supports, and are therefore free to rotate.  Suppose that the left section of the bridge has length 50 meters, total mass 20,000 Kg, and extends a distance of 22 meters to the right of the second support. If vehicles approaching from the left are not to cause the bridge to begin rotating, what is the largest mass that they can have? [8] A hoop of radius R and mass M is released from rest on a decline, as shown below.  After release, the hoop rolls without sliding down the decline. If the initial vertical height of the hoop is 1 meter, determine its speed at the bottom of the decline. Determine how long it takes the hoop to get to the bottom of the decline. [9] Suppose that, in striking a baseball, a bat is in contact with the baseball for precisely 50 ms. If the average force exerted by the bat upon the baseball during this time is 200 N, determine the impulse delivered by the bat to the baseball. Assuming that the mass of the baseball is 150 grams, determine the change in the baseball's speed caused by the impact. [10] From a microscopic perspective, describe what `heat' energy is.