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homework13 - PH 131 FALL 2000 HOMEWORK l3 Assigned Due SE A...

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Unformatted text preview: PH 131 FALL 2000 HOMEWORK # l3 Assigned: 11/27/00 Due: 12/06/00 (( SE. A 140 kg hoop rolls along a horizontal floor so that its center of mass has a speed of 0.150 mls. How much work must be dune on the hoop to step it? ssm 3?. A constant horizontal force of magnitude [0 N is applied to a wheel of mass [0 kg and radius 0.30 m as shown in Fig. 1230. The wheel rolls smoothly on the horizontal surface, and the accel- eration of its center of mass has magnitude 0.60 misz. (a) What are the magnitude and direction of the frictional force on the wheel? (b) What is the rotational inertia of the wheel about the rotation axis titrough its center of mass? 28 :max +1? 241460;”, CHIZ— 25E 25E. Two objects are moving as shown in Fig. 12-35. What is Lheir total angular momentum 6.51:3 about point 0'? ilw ”'2 $39—92? m/s 2 V2. .5 m \7. L? é? @ixfi Q4 2 @1190“ r .3 ~32 @3sz £2 ' £2 2 mafia; 1.2 mm)! :- ww: WWI :: E (3. 0 (5696142) .— (6.90.5)0-291 k3 MML/is :- 51.9; 2.4123725 \ . cot/7: 355 55E, Three particles. each of mass m, are fastened to each other and to a rotation axis at 0 by three massless strings. each with length d as shown in Fig. 126?. The combination rotates around the rotational axis with angular ve- locity w in such a way that the panicies remain in a straight line. In terms of m. d. and w. and rel- ative to point 0, what are (a) the rotational inertia of the combi- nation, (b) the angular momentum of the middle particle. and (c) the total angular momentum of the three particles? 55m GEMIN- R: 0.5-0 rm rm = '0 “3 T; P-eflbd 9% “rota-lb. =25 5 FIND”- (_ao = 5+ruc-lurc's foreliml I” “mew-Hat. and) 0’) «L: Am ulm" mmMu/m éme-{vqrz . 53?. Figure 12-39 shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a con— stant speed about a vertical axis. with _a period of rotation of 2.5 s. ASSuming R = 0.50 m and m = 2.0 kg. calculate (a) the struc- ture‘s rotational inertia about the axis of rotation and (13) its angular momentum about that axis. ' Ca) use. ea. Lt-z‘ttncpgmiml axis Aneofm] from book '- Icw = W- more 92 Circular hoe? atmt «ws 54M- : MEL -l- —_'2- qn’RZ- (us‘ima (tabla 01C P3 . 7.461 in book) :2 % mR'I-u 0 ~ I :- raaw we. bar)+ 1: (Late Vet-{um}. bar) \\ Z + QXIC horizomlaov 54““) mm #093?“ square ll )3 13 75‘ ~52) “'3‘ 1.3, 6; D {J h E 1. r w "G W mm 2—65 " (£1412. - 3‘? E 39E. A man stands on a platform that is rotating (widtout friction} with an angular speed of 1.2 rew‘s; his arms are outstretched and he holds a brick in each hand. The rotational inertia of the system consisting of the man. bricks. and platform about the central axis is 6.0 kg - m3. If by moving the bricks the man decreases the re- tational inertia of the system to 2.0 kg - m3, (at) what is the resulting angular speed of the platform and (b) what is the ratio of the new kinetic energy of the system to the original kinetic energy? (c) What provided the added kinetic energy? 85m $1 Guam-T: 6% .i-L’m Jig—J M ‘l‘k‘l’hl'l‘l‘fl; Lita. aw; . tat/“i L: (OI McMME» Co‘s—meal. - ‘2) Mill KE 50 SHEETS IOO SHEETS 22-144 200 SHEETS 2244] 22-142 @ 48?. A girl of mass M stands on the rim of a frictionless merry—gr» ' round of radius R and rotational inertia I that is not moving. She throws a rock of mass m horizontally in a direction that is tangent to the outer edge of the merry-g0~r0und. The Speed of the rock. relative to the ground, is v. Afterward. what are in) the angular speed of the meny-go-mund and (b) the linear speed of the girl? [a TD? VJELO THE JRL’ lLJMéI'IKZ SPEED 1:9 eat/EM B‘r‘i LONSJMK. g—Axts To BE ALchc-jy _ Kw A710” AXE" (P05. 019'?" 0F PAéE'b W‘— 22-]4] we... 22-142 50 SHEETS 100 SHEETS 22-1 44 200 SHEETS 37V 57P. In Fig. 12415. a 1.0 g bullet is fired into a 0.50 kg block that is mounted on the end of a 0.60 m nonuniform rod of mass 0.50 kg. The block—rod—bullet system then rotates about a fixed axis at point A. The rotational in- ertia of the rod alone about A is 0.060 kg - m3. Assume the block is small enough to treat as a par- ticle on the end of the rod. [3) What is the rotational inertia of the block—rodwbullet system about point A? (b) If the angutar speed of the system about A just Q—u after the builet’s impact is 4.5 Bullet radfs, what is the speed of the bul- 59‘ 1245 Problem 51 let just before the impact? i 15997:?“ " ‘LP—Db + LBLaC-K— rl‘BvLJ—ET h .__ 2 2. 2': Lite!) '9' M r‘ +- MBUH—L’T {— E COMégm/NTJOM 07-“ ANGOLAR MOMEMTUM'. _. __.. aomstbaz z-Axts. To 35 f 1—; = Z. Alf-0&6- ?077 Axis CPDQ. 96)" OF PAéQ) 3 L}?- ‘: Lffi E i - O _ ---'—' i i mbuu-ETVI; FW?O " ‘stsrgm “31° g V- ... Lfiféflzm “DJ:- E I ‘- M0755 - ' L - 1M 0‘ TI?) : BuuaT " Fwd-ET ' = -ts. n—-...._..__-—m~__—— ...
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