4 Solved Problems on Simple Harmonic Motion - Exam 2 | PHYS 1150, Exams of Physics

Download 4 Solved Problems on Simple Harmonic Motion - Exam 2 | PHYS 1150 and more Exams Physics in PDF only on Docsity! GS Exam 2 NAME: Fob dps Physics I Honors, PHYS 1150, Fall 2011 section: This exarti has four questions and you are to work all of them. You must hand in your paper by the end of class time (11:50am) unless prior arrangements have already been mnade with the instructor. You may tse a double-sided equation shéet. You are welcome to use your calculator and an iftegral table. In this exam, with the exception of the multiple-choice problems, you. must show all your work to get credit. As a general rule, you must express your answers in terms of the variables given. E.g., if'a variable Z is given, than the answer should be in terms of Z and Hot £ or d. Good luck! Problem 1: Problem 2: Problem 3: Problem 4: Total: Prebleni 1. (21 pts.) (Multiplé Choice Questions, 3pts each, NO PARTIAL CREDIT) CIRCLE the correct answer. (1.1) A weight suspended from an ideal spring oscillates up and down. if the amplitude of the oscillation is doubled, the period will 1 €! fay emain the same. haa vei ‘B) double. ; (C) halve. fs Lt? bo (D) ittercase by a factor of ¥2. (E) decrease by a factor of V2. lily fe rpbed dle / / (1.2) In sithple harmonic motion, the displacement is maximum whien: (A) tlie acceleration is zero. (B) the velocity is maximum. (©pre velocity is zero. (D) the kinetic energy is maximum. (E) the momentum is maximum. Problem 2. (20pts) A thin ritig of mass Mand radilis Ris placed on a horizontal surface with an initial angular velocity @,. The initial (translational) velocity of the center of mass of the ring is zero. The kinetic frictional coefficient is 42 and the gravitational acceleration is g: ie (ve) = a) OF oe a a —? Lr ze : ie + = MR How long does it take until the ring starts rolling without slippitig? (You must express your answer in terms of the parameters given above.) Me Ma ) Fy ofa Nilig | | \y * air =x Fy i due a i dt f ae? 2 ft ligk 7 i ya f pf" Wg deo ab 4g B ap hl gt — (4@=e) ee tt) wx ~ AEBS — eb FOL Conthen Lo jplliny vurllout “ f “ oo Ele v2 waster LMG Up py obR Ue = WI, ~ LE b | OR sage “Rabe ) JAG OE = R o2, ~g i —~ 6M 7 OD r Reco LE : Tw -- Mg A Sue here, adel \ Problem 3. (20pts) A pliysical pendulum consists of a thin solid disc of mass M and radius R with its center attached to a thin rod of lengih 2R and negligible mass. The pendulum can rotate freely in a vertical plane about an axis going through the other end of the rod. The gravitational acceleration is g. a wlIF SL Mee LMR ger 2 Me Z What is the period of this pendulum for small oscillations? (Yott must express your answer using the parameters given above.) ; ue No f1g4 tar / e LO x Ligd ( Cag shiek WA L! 4 bs Caprei on / Problem 4. (20pts) Witli a solid metal block of volume V,, and density p,, we are trylitg to hold down (ina tank of water) a plastic object of volume V, and density p, (they are connected by a massless thin string). All objects are filly immersed iti water (which has density 6, > p,) as illustrated below. The gravitational acceleraticti is g - wudel bob: Nmret 7 (9) vba Be t (a) [iSpis] If the metal block stays at the bottom (as illustrated iri the figure), what is the normal fotce N exerted by the bottom of the tank on the metal block? You must express you answer in terms of Vy,, Py, Vp +» Pp» Py, andg. mebl bbes ; M ~ fia G the Ya grt =- © pooh i “Ios g-T =° Me - fa Yn Gothaba g - [ve Qo “bey B+ (o~ Pao 9 pee é ce object : (b) [Spts] ‘For given values of V,,, Vp, pp, and py, what is the minimum required density of the metal block p;, so that it stays down at the bottom? You must express you ansWer ititerms of Vy, V,, pp,and py. [N>ef (is fle bey enol dant) (hn fe) Via > foe fo) Up fy a fot betel = pe