PHY 213 Exam 3: Rotational Motion November 9, 2020 Name ____________________________________________________________ INSTRUCTIONS: • This examination consists of 6 multiple choice questions (4 points each), two short answer (5 points each), a rank task/TIPER question (6 points), and 3 workout problems (20 points each). • You may use a non-graphing calculator for the exam. You may not have your phone out during the exam. • You may use g=10 m/s2 to simplify your calculations if you wish. TO EARN CREDIT YOU HAVE TO SHOW ALL YOUR WORK Do not write below this line 6 Multiple Choice (24 pts) Short Answer (10 pts) _________ Ranking Task (6 pts) _________ Workout 1 (20 pts) Workout 2 (20 pts) Workout 3 (20 pts) Extra Credit (5 pts) TOTAL (100 pts) _________ 1 PHY 213 Exam 3: Rotational Motion November 9, 2020 2 PHY 213 Exam 3: Rotational Motion November 9, 2020 Some possibly useful formulas and constants: ! !" π()* = +! $+" ,! $," % x # = nx #$% g ≈ 10 m/s ' π()* = -! $-" ,! $," ∫ x # dx = #&% x #&% + constant G ≈ 6.67 × 10$%% N β m' /kg ' ' π+' − π.+ = 2π+ (π₯ − π₯. ) πΉ345 = ππ πΉ = −ππ₯ % πΎ = ' ππ ' π/01, = π6 = π6 π <latexit sha1_base64="s6IA3dw6VNYl/wpHGoT80gFLLwQ=">AAACBnicbVBNS8NAEN3Ur1q/oh5FWCyCp5JUQS9CURCPFWwrNKFsNpN26WYTdjeFUnry4l/x4kERr/4Gb/4bt20O2vpg4e17M8zMC1LOlHacb6uwtLyyulZcL21sbm3v2Lt7TZVkkkKDJjyRDwFRwJmAhmaaw0MqgcQBh1bQv574rQFIxRJxr4cp+DHpChYxSrSROvZhC19ijwmNvQFQfIM9Gib5J1Qdu+xUnCnwInFzUkY56h37ywsTmsUgNOVEqbbrpNofEakZ5TAueZmClNA+6ULbUEFiUP5oesYYHxslxFEizTMLTdXfHSMSKzWMA1MZE91T895E/M9rZzq68EdMpJkGQWeDooxjneBJJjhkEqjmQ0MIlczsimmPSEK1Sa5kQnDnT14kzWrFPa1U787Ktas8jiI6QEfoBLnoHNXQLaqjBqLoET2jV/RmPVkv1rv1MSstWHnPPvoD6/MHhqSXQw==</latexit> Z ) Wtot = βπΎπΈ βπβ πΉβ345 = Vβπ‘ πβ = ππβ ∑ B" $ π345 = πΌπΌ π = πC πΉ = ππΉC = ππΉπ πππ π = π. + πΌπ‘ π = π. + π. π‘ + ' πΌπ‘ ' βπβ = πΉβ()* βπ‘ ∑ B " +" πΌ'#!*+* = , ππ $ % πΉ8 .1 : = −πΉ: .1 8 π*2()=,> = ππβ π₯?@ = πΌ%&'( = $ ππ $ π = ππΌ ~ F~ · ds % βπΈ = π3? π = ππ 2 π7 ≤ π7 π π;<2=1* = ' ππ₯ ' cm moments of inertia: πΌ!""# = ππ $ -# π = πΉ+ βπ₯ = πΉπππ πβπ₯ W = πΈ = πΎ + π*2()=,> + π;<2=1* % π₯ = π₯. + π.+ π‘ + ' π+ π‘ ' π+ = π.+ + π+ π‘ % ) πΌ+"% = )$ ππΏ$ % ' πΎ = ' ππ?@ + ' πΌ?@ π' π' − π.' = 2πΌ(π − π. ) π!"# = $- %$. &- %&. πΌ = πΌ?@ + πβ' 3 PHY 213 Exam 3: Rotational Motion November 9, 2020 4 PHY 213 Exam 3: Rotational Motion November 9, 2020 Multiple Choice Questions: 1. A woman stands on the very end of a 50 kg uniform board of length 12 ft, which is supported at 3 ft from one end and is balanced. What is the mass of the woman? a) b) c) d) e) 40 kg 50 kg 60 kg 80 kg 100 kg 2. In both cases the beam has the same mass and length and is attached to the wall by a hinge. In which of the static cases shown is the tension in the supporting wire bigger? a) Case 1 b) Case 2 c) Same 3. A disc spins on an axis and is observed to have a constant angular velocity, then it has: a) a zero net torque b) a constant net torque c) an increasing net torque d) a constant angular acceleration e) an increasing angular acceleration 4 A wheel which is initially at rest starts to turn with a constant angular acceleration. After 3 seconds it has made 2 complete revolutions. How many total revolutions has it made after 6 seconds? a) 2 b) 4 c) 6 d) 8 e) 12 5 PHY 213 Exam 3: Rotational Motion November 9, 2020 5. A wrench has a mass of 0.5 kg, and a moment of inertia around its center-of-mass of ICM=20.0 kg cm2. If it is rotated about an end which is 10 cm from the center of mass, what is the moment of inertia about this axis? a. 5 kg cm2 b. 20 kg cm2 c. 25 kg cm2 d. 50 kg cm2 e. 70 kg cm2 6. On a digital video disc (DVD), video and audio data are stored in a series of tiny pits that are evenly spaced along a long spiral that spans most of the surface of the disc and extends from the inner edge of the DVD to the outer edge. The scanning laser in a DVD player reads this information at a constant rate. As the player reads information recorded closer and closer to the outer edge of the DVD, the disc should a) rotate faster b) rotate slower c) rotate at the same speed 6 PHY 213 Exam 3: Rotational Motion November 9, 2020 Short Answer (5 points each): 1a. When reducing the mass of a racing bike, the greatest benefit is realized from reducing the mass of the tires and wheel rims. Why does this allow a racer to achieve greater accelerations than would an identical reduction in the mass of the bicycle’s frame? 1b. Suppose a piece of food is on the edge of a rotating microwave oven plate. Does it experience nonzero tangential acceleration, centripetal acceleration, or both when: (a) the plate starts to spin faster? (b) The plate rotates at constant angular velocity? (c) The plate slows to a halt? If the food experiences these accelerations, make sure to give their direction. 2. Calculate the torques of the five forces acting on the metal bar below. Each force has a magnitude of 10 N and the bar has a length of 2.5m. Don’t forget to include direction. ________________________ ____________________ ________________________ ____________________ _________________________ 7 PHY 213 Exam 3: Rotational Motion November 9, 2020 Ranking Task/TIPER Question (6 pts): 8 PHY 213 Exam 3: Rotational Motion November 9, 2020 Workout Question #1: A solid disk (mass = 5 kg, radius = 20 cm, height = 5 cm) has four 0.5-kg masses attached around the outside edge as shown. The disk is mounted on an axle at its center and a thin rope wrapped around the outer edge. You pull on the rope with a constant force. After 10 seconds, the masses are moving with a tangential speed of 5 m/s. a) What is the moment of inertia of the system (disk and four masses)? b) After 5 seconds, what is the angular velocity of the disk? c) What is the magnitude of the torque you exert? d) What is the magnitude of the force you are pulling with? e) What is the change in kinetic energy of the disk during these 10 seconds? 9 PHY 213 Exam 3: Rotational Motion November 9, 2020 Workout Question #2: A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle π = 20Λ. The sphere has mass M = 2.5 kg and radius R = 0.50 m. The coefficients of kinetic and static friction between the sphere and the plane are π( = 0.15, π' = 0.25. a) Draw a free-body diagram for the sphere. b) Calculate the magnitude of the acceleration of the center of mass of the sphere. c) What is the force of friction on the sphere? Now, the ball is started from a different condition. It is given a push down the incline so that it has no initial rotational speed, and is initially slipping. d) Calculate the magnitude of the acceleration of the center of sphere. e) Calculate the magnitude of the angular acceleration of the sphere. 10 PHY 213 Exam 3: Rotational Motion November 9, 2020 Workout Question #3: Sir Lancelot rides slowly out of the castle at Camelot and onto the L = 12.0 m long drawbridge that passes over the moat. Unbeknownst to him, his enemies have secretly partially severed the drawbridge cable holding up the front end of the drawbridge (which makes an angle of q=25.9° with the drawbridge as show below) so that it will break under a tension of 1.2x104 N. The drawbridge has a mass of 200 kg. Sir Lancelot, his lance, his armor, and his horse together have a combined mass of 600 kg. a) Will the cable break before Sir Lancelot reaches the end of the drawbridge? If so, how far from the castle end of the bridge will the Sir Lancelot be when the cable breaks? b) What is the force that the hinge exerts on the drawbridge at (depending on your answer to part a)) either the moment when the drawbridge cable is about to break or when Lancelot reaches the end of the drawbridge 11 PHY 213 Exam 3: Rotational Motion November 9, 2020 Extra Credit [5 points]: One end of a post weighing 400N and with total length L rests on a rough horizontal surface with s = 0.30. The upper end is held by a rope fastened to the surface and making an angle of 36.98 with the post. A horizontal force F is exerted on the post as shown at a height h. In this problem we’re interested in the maximum force F = Fmax that can be applied to the post before it begins to slip. a) Draw a free-body diagram for the post. b) Using the conditions for rotational statics, write down equations for SFx, SFy, and St. c) Find the normal force acting on the post. d) Solve for the tension in the rope in terms of the force Fmax. 12