Physics 2210 Fall November 21 David Ailion

Transcription

1 I...i*'.lF"'.JOf_,.,rwWJl';_...*;iIIi:~ Physics 2210 Fall November 21 David Ailion Unid: = Discussion TA:8 Justin Will Yuan 1 Place answers in box provided for each question. SpecifY units for each answer. Place answers in box provided for each question! A. [5 pis'] Which of the following are true. i IC,d( ;; Angular momentum is always conserved. Angular momentum is always conserved provided the internal torques cancel one another. For a macroscopic object, internal torques cancel one another. The external torque on a macroscopic system equals the rate of change of its angular momentum. None ofthe above are true. B. [5 pis'] A rigid thin rod of length L rotates about an axis perpendicular to the rod axis...r , j with one end ofthe rod fixed to the axis (as shown in the drawing). Which ofthe 01( following are equal at all points on the rod? L I The angular position. The angular velocity. The angular acceleration. (d) The centripetal acceleration. (e) The tangential acceleration. c. [5 pts.] Two identical bowling balls are each rolling with the same initial velocity on the same floor. At a particular point on the floor, ball A encounters a smooth inclined plane. After going the same distance on the floor, ball B encounters a rough inclined plane (Le., no slipping) having the same inclination angle. Which balls goes higher on the plane? A) -l y1'1v J +JI('l?':: J'11;,h t 1Iw J Ball A.. 1. Zf )j. 2 ~ Ball B.. 13) 1/1vJ.t-l.JV)~ ~ rn.9j} Both balls reach the same maximum height. ~ f~ (d) You need to know the velocity and the angle ofthe plane to answer this.

2 -- ---" Physics 2210 Fall November 21 David Ailion Unid: Discussion TA:e Justin Will Yuan Problem 1 ~ Continued y D. [5 pis'] Consider the following collection of 5 mass points. Give the x and y components ofthe center-of-mass vector relative to the indicated origin. "em = ~ I I t3 a a a () t) I 2: x; Pit" :: ;~~) -d"~i4j) t~~)! ~I) r :ktlm) }q m - }I111 """' 1/ ~ 9B~ -w.;) +~)- bk3~ t OCi11} o I ) I1J 2m 3m E. [5 pis'] The figure shows a planet traveling in a clockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A, - J:2 (@) (d) the speed is constant. the speed is increasing. the speed is decreasing. the speed is a maximum. (e) the speed is a minimum. '... b \

3 Fall NO\ emher 21 1>.., id.\iliol Vnid: Discussion TA: Bryant Justin Will Yuan 2 RePOrt all numbers to two significant figures. A rigid, massless rod has three particles with equal masses attached to it as shown. The rod is free to rotate in a vertical plane about a frictionless axle perpendicular to the rod through the point P and is released from rest in the horizontal position at t = O. Assume that m and d are known. (Use the following as necessary: m, d, and g.) (b) (d) (e)

4 ~ ' Name: Y ltlt') Vnid: Discussion T A: Bryant Justin Will Yuan 3 Place a circle or box around each answer. S!>ecify units for each answer. Report all Dumbers to two significant figures. m Consider a solid cylinder of mass m and radius r that is rolling without slipping down a rough plane of angle e. Assume that the cylinder starts rolling from rest with its center at a height h above the end of the plane. h (b) [10 pis.} Calculate the speed of the center of mass in terms ofm. g, h and r when the cylinder reaches the bottom ofthe plane. [7 pts.} Calculate the acceleration ofthe center of mass at point P in terms of the given quantities. [8 pts.} Calculate f, the force offriction at point P, in terms ofthe given quantities. Specify whether the friction is static or kinetic. I:" E; -:: vf (a') r>1jh -= ±n, v,..,.. t 1 tn~ 1- h1 '(2. w:::: 2.. ' YhcfJ.r~ 1-~" V~ -I- ~ ~ V' V = m,*i) v. = 2~ ~

5 Ph~'sics 2210 Fall co JllII'I Name: Idil) Vnid: ~ Discussion TA: Bryant Justin Will Yuan 4 m_<lllli m Consider a double star system consisting oftwo identical stars, each of mass m and radius r, whose centers of are separated by a distance R. Assume that the orbit of each star is a circle, and that the ~ions of the stars about their axes can be neglected.,t.. ~~ '~~f "'[7piS.] Calculate the total energy of the system in terms of given quantities (G, m, R, r). '(b) '," j:zpis.j Calculate the total angular momentum about the common center of mass in terms of the given quantities.. (cj;.~:-.[./tl pis) Suddenly one of the stars ejects a small amount of material Am in a direction that is along the line joining the!\yo s~s but away from both (as shown). Derive an expression for the escape speed ofthe mass Am from the system. For this part, neglect the motion of the stars m m ~m ~,{2... _ ~ V 11 k = -A L{ y/_ '~,~_~, _yro Fe;. := 1A ~II\ V).. L{,' -= - G,.1 V'1~ - G.b ii'1 IN\ I f G J:::i'f V'v\ (;fi VIA... ~~~r~------~ , Ij= j:zc;m(+ + ~ _...