Physics 218 - Exam P3 April 17th , 2015 Please read the instructions below, but do not open the exam until told to do so. Rules of the exam: 1. You have 75 minutes to complete the exam. 2. Formulae are provided on the last page. You may NOT use any other formula sheet. 3. You may use any type of handheld calculator. However, you MUST show your work. If you do not show HOW you integrated or HOW you took the derivative or HOW you solved a quadratic or system of equations, etc, you will NOT get credit. 4. Cell phone use during the exam is strictly prohibited. 5. Be sure to put a box around your final answers and clearly indicate your work. 6. Partial credit can be given ONLY if your work is clearly explained and labeled. NO credit will be given unless we can determine which answer you are choosing, or which answer you wish us to consider. If the answer marked does not follow from the work shown, even if it is correct, you will not get credit for the answer. 7. You do not need to show work for the multiple choice questions. 8. Have your TAMU ID ready when submitting your exam to the proctor. 9. Check to see that there are 6 pages + 1 formula sheet. 10. If you need extra space, use the reverse side to complete your work and indicate/mark on the main page of the problem that you are continuing on the reverse side. 11. DO NOT REMOVE ANY PAGES FROM THIS BOOKLET. Sign below to indicate you understanding of the above rules. Name : .................................................................................. Section Number : .................................................................................. Instructor’s Name : .................................................................................. Signature : .................................................................................. Short Problems (Circle the correct option - NO PARTIAL CREDIT) [20 Points] A) [5 points] A hollow sphere (a), a solid sphere (b), and a thin hoop (c) all with the same mass and radius are having a race. They roll without slipping down a 30° incline starting at a height h. Rank the time it takes each of them to roll down the hill from greatest to least. i) ta > tb > tc ii) ta > tc > tb iii) tc > ta > tb iv) tc > tb > ta v) tb > tc > ta vi) tb > ta > tc vii) The correct answer is not shown. B) [5 points] A 2 kg rock has a horizontal velocity of 12 m/s when it is at the point P (x, y, z) = √ (−6 3, 6, 0). At this point, what is the magnitude of its angular momentum relative to the origin? i) 17 kg m2 /s ii) 144 kg m2 /s √ iii) 106 3 kg m2 /s iv) 297 kg m2 /s v) 9001 kg m2 /s vi) The correct answer is not shown. C) [5 points] Merril Lehrl (70 kg) sits on the midpoint of a board protruding horizontally from a wall. The board has a length of 17 m and a mass of 140 kg. The board is also attached to the wall via a string stretching from the wall to the opposite end of the board such that it makes an angle θ at their intersection. If the tension in the string is measured to be 2060.1 N, what is θ? i) 0° ii) 30° iii) 45° iv) 60° v) 90° vi) 297° vii) The correct is not shown. D) [5 points] A loose cannon Dutch cop who refuses to play by the rules jumps from a levee with an initial horizontal velocity v0 . After gracefully soaring a horizontal distance D, he reaches out and grabs a windmill. The blade has a radius R and is perfectly horizontal. Assuming the windmill was initially at rest, calculate its new angular momentum just after the collision in terms D, R, v0 , the mass of the cop m, and constants. i) L = mgv0 DR ii) L = v0 mgDR iii) L = mgDR v0 iv) L = mg v0 DR v) The correct answer is not shown. vi) The correct answer is never shown. Problem 2 [20 Points] Biggie recently installed a pool beneath his Goat Tower. So Biggie walks out on to the diving board and does a front flip off the board. He starts out with his front and hind legs straight, so we can treat him like a solid cube with a mass mb = 20 kg and side length l = 2 m, rotating about its center of mass1 with an angular speed of ω0 = 4 rev/s. a) He then curls up into a solid ball of radius rb = 2 m.2 What is his new angular speed? b) Suppose he curls up into the sphere at the very peak of his jump, 15 m above the pool. How many revolutions does he complete before he strikes the water? 1I cm 2 = I= ml2 for a cube. 6 2mr2 5 Problem 3 [20 Points] Tiny the goat sits atop a uniform ladder of length l and of mass ml resting on a freshly painted wall such that the base of the ladder makes an angle θ with the horizontal. The fresh paint makes the surface of the wall very slippery, so friction between the ladder and the wall can be ignored. Tiny, unlike Biggie, HAS been going to the gym and has a mass mt . To ensure that Tiny doesn’t fall to his death, what is the minimum coefficient of static friction between the base of the ladder and the ground? Problem 4 [20 Points] Biggie the goat has just unveiled his latest ‘art’ installation! It is a kinetic sculpture that consists of two alfalfa pies stuck together and hung vertically from a wall. The outer pie has a radius RD and is firmly fixed onto the inner pie of radius RA such that the two pies have a common axis. About this axis, the pies have moments of inertia ID and IA respectively. The pies are free to rotate about their common center. A massless cord is wrapped around the inner pie and attached to a tin can of mass m1 . A similar cord is wrapped around the outer pie in the opposite direction and attached to a potato of mass m2 . Assuming the cords do not slip, find the acceleration of the potato. Problem 5 [20 Points] Biggie the goat decided to dig to center of the Earth one day. After he had dug a quarter of the way there, he took a break. Then his friend, Tiny the goat, dropped a flowerpot of mass mp = 300 g on Biggie for laughs. For reference, the mass of the earth is mE = 5.97∗1024 kg, its radius is RE = 6.37∗106 m, and air resistance is negligible. a) Knowing that the density of the Earth is roughly constant (ρ = 5.51 ∗ 103 kg/m3 ), get an expression for the force of gravity as a function of r felt by the flowerpot as it falls through the Earth. HINT: the only mass that matters is that which is ’below’ the flowerpot, so we’re going to need to calculate the fraction of mass that’s below the flowerpot at a radius r. b) Supposing the flowerpot is dropped from rest, calculate the velocity of the flower pot when it strikes Biggie. Will it hurt? c) Furious, Biggie launches the flowerpot so hard that it reaches escape velocity. With what velocity did Biggie throw the flower pot?3 3 As a reminder, escape velocity is defined as when an object’s final potential and kinetic energy go to zero.
© Copyright 2024