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Physics 123 Fall 2009 – Document #16: Homework #08 & Reading Assignment page 1 of 6 PHYS 123: Homework #08 and Reading Assignment October 21, 2009 This homework due just outside of Mr. Covault’s Ofﬁce: Rock 207, 5:00 PM Sharp, Monday, October 26, 2009 Announcements: • If you wish a Re-grade for the First or Second Hour Exam, please follow directions indicated in Handout #12. Homework and Reading Assignment continues next page.... Physics 123 Fall 2009 – Document #16: Homework #08 & Reading Assignment page 2 of 6 Physics 123: Fall 2009: Week 9 Reading assignment: Please try to complete the following reading by Wednesday, October 28th: REQUIRED: Read Introduction to Mechanics by Kleppner and Kolenkow as follows: • Read selected sections of Chapter 6 as follows. – Read Sections 6.1 through 6.7. Take your time and make notes of anything you do not understand. • Read selected sections of Chapter 7 as follows. – Read Sections 7.1 through 7.6. Take your time and make notes of anything you do not understand. Homework continues next page.... Physics 123 Fall 2009 – Document #16: Homework #08 & Reading Assignment page 3 of 6 Physics 123: Fall 2009: Homework #08 This homework due just outside of Rock 207: 5 PM Sharp, Monday, October 26, 2009 Important note: The homework will be graded on a scale of 0 to 15 points. Not all problems will always be graded. Problems 1, 2, and3 : Please re-answer the three problems on the Second Hour Exam. For each of the three problem choose one of these: • You may re-work the problem “from scratch”. • If you scored within 10% of the points awarded on a given problem you may chose to indicate this. No further work is required. However, if you feel that a your solution is not the most elegant solution possible, please solve the problem in the most elegant way. Note: obviously since the solutions to the exam are posted, you are free to study these to help you do this homework assignment. But you should try to solve each problem as far as you can before checking the solution since your goal is to be able to work each problem on your own. Problem 4 : Please write a short essay (maybe one but certainly not more than two pages) on this question: What can be done to improve the Hour Exam test scores for Physics 123? You should consider things that you could do that would help. You should consider things that the instructor could do that would help. Try to be as speciﬁc and personal as possible with respect to what happened to you on the Second Hour exam. For example, “I would have done better on Problem 1, if only....” Please use word processor or email or (neat) handwriting. Alternatively, if you performance improved on the Second Hour Exam relative to the First Hour exam, feel free to address the following question instead of or in addition to the question above: What steps did you take that were particular helpful to you in terms of improving your performance on the recent exam? Physics 123 Fall 2009 – Document #16: Homework #08 & Reading Assignment Problem 5 : page 4 of 6 P θ S A solid metallic sphere is placed on the top of a ramp as shown above and then rolls without slipping down the ramp, past point P to the bottom of the ramp at point Q. The angle of the ramp is given as θ. The initial position of the sphere is unknown, but the distance between P and Q is given by L and the speed of the sphere at point P is measured to be vp . The rotational inertia of the 2 sphere sphere is Is = 5 mR2 where m is the mass of the sphere and R is the radius of the sphere. Again, assume that θ, L, vp , m, and R are all given and that the initial starting position of sphere is unknown. Neglect air resistance. Part (a): Determine the linear speed of the sphere vq when it reaches point Q. Your answer should be in terms of the given parameters. Explain your work. Part (b): Conceptual question: Suppose that we replace the solid shell with a hollow spherical shell that has half the mass of the solid sphere but the same radius. What will be the impact of this change on the calculated speed vq at point Q? Will the hollow shell be going faster, slower, or at exactly the same speed as we calculated for the solid sphere in Part (a)? Explain. Hint: You do not need to know the exact value of the rotational inertia of a hollow shell to determine the answer to this problem. No detailed calculations are required for this part. Part (c): Harder: For the problem as stated in Part (a), if we assume that the sphere rolls without slipping, what can we say – if anything – about the value of the coefﬁcient of static friction µs ? Can we determine the value of µs exactly? If, so, what is it? If not, can we place any constraints on it’s value? If so, what are these constraints? Or is the value of µs completely unknown and unconstrained (except for the obvious physical requirement that µs > 0)? Explain. Physics 123 Fall 2009 – Document #16: Homework #08 & Reading Assignment Problem 6 : page 5 of 6 ice Schrodinger Einstein On a warm day in late winter Schrodinger is tired of playing with his cat. He takes his dog, Einstein to the lake which has frozen into glare ice (virtually no friction). Einstein stands on the frozen lake and Schrodinger stands on the shore and throws a Frisbee ﬂying disk to him. The mass of the disk is 1.43 kg. The radius of the disk is 12.4 cm. The disk leaves Schrodinger’s hand with a translational velocity of 6.37 meters per second and a rotational speed of 14.21 radians per second. Einstein catches the frisbee. His mass is 31.3 kg and his moment of inertia is 40 times that of the Frisbee. For this problem (except possibly for part e) assume that the Frisbee travels in a straight horizontal line and ignore any vertical components of the motion of the Frisbee. Also ignore any horizontal forces due to air friction. Part (a): What is Einstein’s rotational velocity after catching the Frisbee? Explain your answer. Part (b): What is the total kinetic energy of the Frisbee after it is thrown? Part (c): What is the velocity of the center-of-mass vcm for the Frisbee-Einstein system after the Frisbee has been caught, as seen in Schrodinger’s frame of reference? Part (d): What is the velocity of the center-of-mass vcm for the Frisbee-Einstein system after the Frisbee has been caught as seen in Einstein’s frame of reference? Part (e): The Frisbee will not ﬂy properly unless it is thrown with considerable spin. Explain this fact in three sentences or less. Hint: your answer should have something to do with angular momentum. Physics 123 Fall 2009 – Document #16: Homework #08 & Reading Assignment Problem 7 : page 6 of 6 hinge θ max gravity v v’ A thin rod of mass M and length L hangs vertically from the ceiling attached to an ideal hinge. A small bullet with mass m strikes the rod horizontally at a point ℓ from the hinge. The bullet pokes a hole right through the rod. The speed of the bullet before the impact was v and the speed after the impact was v ′ . What is θmax corresponding to the maximum swing angle of the rod after impact? Ignore any effect of gravity on the bullet. Problem 8 : Consider the elliptical orbit of a comet mass mc around the sun mass Ms as shown: A Ra Rb B Point A on the orbit represents the closest approach of the comet at a distance of Ra from the sun. Point B is where the comet is furthest from the sun, at distance Rb . The speed of the comet at point A is va . Part (a) What is the speed of the comet at point B? For this problem assume you do know neither the mass of the comet, nor the mass of the sun. Part (b) Can you show that your result is consistent with at least one of Kepler’s three laws?