Height of Block - Introductory Physics - Solved Paper, Exams of Physics

Download Height of Block - Introductory Physics - Solved Paper and more Exams Physics in PDF only on Docsity! FROM : : FAX NO. = Apr. 14 2683 @8:47AM PI University of California at Berkeley Department of Physics Physics 8A, Spring 2003 Second Midterm Exam April 9, 2003 You will be given 120 minutes to work this exam. No books, but you may use a . handwritten note sheet no larger than an 8 1/2 by 11 sheet of paper. Your description of the physics involved in a problem is worth significantly more than any numerical answer. + Show all work, and take particular care to explain what you are doing. Write your answers directly on the exam, and if you have to use the back of a sheet make sure to put a note on the front. Do not use a blue book or scratch paper. sin 45° = 0.707, cos 45° = 0.707, sin 30° = 0.500, cas 30° = 0.866 Rotational Inertias for radius R or length L: sphere about axis: (2/SyMR2 spherical shell about axis: (2/3)MR2 disk about axis: (1/2)MR2 hoop about axis: MR2 rod about perpendicular at midpoint: ML2/12 1 = = 3ev" + yg +P ~ constant ae x o= ii SF-ma Bach part is worth the number of points indicated. These should sum to 100 paints. Setup and explanation are worth almost all the of the points. Clearly state what you are doing and why. In particular, make sure that you explain what principles and conservation rules you are applying, and how they relate. L 1 name: ___©©¢ te re! 2 _— Solutions — SID NUMBER: ° t f 3 DISCUSSION SECTION NUMBER. 4 DISCUSSION SECTION DATE/TIME: 3 6 Read the problems carefully. Try to do all the problems. fig ? If you get stuck, go on to the next problem. ‘otal || yA 5 Dont give up! Try to remain relaxed and work steadily. | ——— FROM = _ FAX NO. = Apr. 14 2683 @8:47AM Pe 1) (25 points) A cylindrical block of wood with radius R, total length L and density ¢, is floating in a liquid of density Py See figure. a) Find the height of the block above the surface. This is marked as h in the figure. ~ b) The block is lifted a small distance x and released (“Small means that x<<h). The How long does it take to go through one complete block then bobs up and down. cycle? A Fe = PEL o foe We h) eed Aa. a m= RK CH) Oo L mg. peELh) Pa PATO & ge Fb - Wy =e, (eWer- LO = o Le -h@e -L@, ° eee ~P LC%~ Pe) ee. & lo sunple hawenie mehen, T= 2y, > am Von and K= fone Feggarted $o displace the aster Where m= R46 L@e 1 uit amount CL), Te + md ley lelts suppese tek the bled mato 1 unt arent ote 4 oece , Fe ae has ben apple : Te LP tes Fe-Fe mg = 0 t Fo= R°TCL-b4+ Lunt) Ce 4 - 1 umnts ing , tng= RT CLD Pog Finoen on pened y MB = REN Che 4. $e: ROU tht tunt) eg 4- Fe - Be TeLh er 4, =O. . R? TWO tuaik) Pe -9, = Fe Se WH ayy a BES CIMA, energy TJe2tley = 27 RTOR _ (% ae - FROM : FAM NO. : Apr. 14 2683 G8:49AM PS 4) (20 points) A work platform is hung from the new Bay Bridge by two cables. The platform is positioned by shortening ard lengthening the cables, so the cables may not be the same length. One cable has tension T, and makes an angle of 0, with the vertical. The other bas tension T, and makes an angle of @, with the vertical (see figure). Find an expression for T,, the tension in cable 1, that does nat depend on T,. Conte! foule 2 > In equionum ‘Bane =? Ey per = 2 Tap =O eo. . Vise sry Fieyran of the E Flat Berm. nak FO o- Tex +Tex =e Tt —Tisptiirt Thnb = 0 - + = 1 eek f aa SVB. Fyne = 0 “Tix | Tey a2) Mpg, aTy + Tay meg oe § hey 4 Ti es tT, foo Se TeaTen@, Tees Ta Oe TF Thue Tices@, “RBy= eos Gy Meg, =~ 12 Gs C81 Case, Coser Eno ae, e, Tr * mw ‘ Ree _ — we \(SS ) TT =m ‘ em = TT, Susiesoe fs 1 Sn@z ws Oi TT = ba ype Los C [+ S28 8: ) ae Gy, Cosei+ a) Sta Oa, FROM : : FAx NO. : Apr. 14 2803 8:49AM PS 5) (20 points) Two point-like children of mass m,=20kg and m,=25kg are each sitting L=2 meters from the center of a see-saw (see figure), The mass of the see-saw plank is M,=60kg. Use 10 m/s? for g. At the moment shown in the figure, what is the angular acbeleration of the see-saw? Specify magnitude and direction. Please do the problem symbolically before plugging in any numbers, and use the symbols listed abave. ol \ l we able e Sat : Ne Me a 4 +———_-+1 au 2n + Trak = CEs Dnt = Tol. CAD me = Crm ae + megs 10) [ing te) VgoeNm + FO = Bort n “leon em gc re sctcwsis.2 rerggae) CED ur Lnet = Trea + Em + Dome Ipp = my = Long: dm dif, = adicgm* Tm = mer = Zot Cn)* Typ Be + Betmo 766 eq? = 260 pen & TL z Vim = MEO So ULPles Clin)? = [pe key mt, CFA ne + Lan Lf, = foon py 2hoky m* zt Ee ce é vad fe (a8 dts?) heb eloclers ise. dey accel. FROM : FAX NO. + Apr. 14 2083 G8:58AM PY 6) (10 points) Water is moving through a pipe of radius R, until it comes to 4 nozzle of radius Rj, It passes through the nozzle at velocity v, and exits at atmospheric pressure. ‘What is the pressure in the pipe at point A in the figure? Please ignore frictional losses in the fluid. A y Moarle Ry AM = Aas : (ue, 7 (Tete | = Bt © ‘ we Re Ve 4 Bernehhi 'S He. Ptbeve + egy. Pat dent+eoya 4a =o, vx Bova Cfrom preasat ) | Pao Fn Foe Bem t@woter yew 4 Auate- SS le ~ Pam + $ esate [1-22] “ad 7