Physics: Dr. F. Wilhelm E:\Excel files\130\m3a Sp06 130a solved.doc page 1 of 9
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1 Physics: D. F. Wilhelm E:\Excel files\130\m3a Sp06 130a solved.doc page 1 of 9 NAME:... POINTS:... D. Fitz Wilhelm, Diablo Valley College, Physics Depatment Phone: (95) Extension: 403 Midtem 3a, ch. 10-1, Physics130, May 1, 006 NOTE: TO ENSURE FULL CREDIT EMPHASIZE YOUR ANSWERS AND INCLUDE DIMENSIONS. SPECIFY WHICH PRINCIPLES OR LAWS YOU ARE USING. EXPLAIN BRIEFLY WHAT YOU ARE TRYING TO DO. ORGANIZE YOUR WORK LOGICALLY. USE DRAWINGS! Use the coect numbe of significant figues G = ; h= ;R = m; M = kg; M = kg; e 30 8 m MeV Msun = kg; c= ;1eV = J; melecton = kg = s c h 34 m p = hk; E = hω : ΔxΔp ; h= Js; H = ; Ycoppe = p; Bcoppe = sl ightyeas moon m kg vsound = 331 ρai = and 1 ; 3 at C atm P max = ρvi; s m eath p 1. A mete stick of mass.00e gams is suspended at the 60.0 cm mak in such a way that it can feely otate aound this point. It is eleased fom an initial angle of 11.0 degees with the vetical. [3] Fist calculate the moment of inetia of the stick. 1.87E-kgm [] Find its peiod of oscillation. 1.93s [5] What is the speed of the endpoint (at the longe adius), when the mete stick has its geatest angula velocity. Use the equations of simple hamonic motion m/s
2 Physics: D. F. Wilhelm E:\Excel files\130\m3a Sp06 130a solved.doc page of 9 5. [10] Find the five solutions of the complex equation z ˆ = + i3. Calculate the second solution (fo n=) in the fom of a + ib. Use thee significant figues nπ i( ) 5 z = 1.9e n= 0,1,,3,4 z n = i 3 [10] A sphee of mass 3.00 kg and a adius of 4.60 cm olls down a plane inclined by the angle of 4.0 degees with the hoizontal. Find the minimum coefficient of static fiction fo this sphee to oll without slipping. Make a dawing and clealy show the foces and toques you ae using. 5 sin.85 / a = g θ = m s 7 a μ = tanθ = 0.17 g sinθ
3 Physics: D. F. Wilhelm E:\Excel files\130\m3a Sp06 130a solved.doc page 3 of 9 4 [10] A beam of length L and mass m is held against a wall by a sting which makes an angle of θ as shown. At a point located at 0.9 times the length of the beam a mass times geate than the mass of the beam is suspended. The coefficient of static fiction between the wall and the beam is μ. By using the conditions of equilibium fo the beam find an expession fo μ as a function of the angle θ. θ μ=7/3 tanθ 5. [10] An electic moto tuns a flywheel though a dive belt that joins a pulley on the moto and a pulley that is igidly attached to the flywheel. The flywheel is a solid disk with a mass of 15 kg and a adius of 65.0 cm. It tuns on a fictionless axle. Its pulley has a neglible mass and a adius of 0.10 m. If the tension in the uppe (taut) segment of the belt is 470 N, and the flywheel has an angula acceleation of.67 ad/s, find the tension in the lowe (slack) segment of the belt. T L =134N
4 Physics: D. F. Wilhelm E:\Excel files\130\m3a Sp06 130a solved.doc page 4 of 9 6) A steel cable of length 1.0 m and density 66.5g/m is put unde a tension of 1.5 E4 Newtons. [5] Find the speed of a wave in that wie. 434m/s [5] Wite down the equation of the wave which tavels in this cable fom left to ight with a wavelength of 1.50 cm Assume the amplitude is cm E5 y = 0.300cm sin x t) m s
5 Physics: D. F. Wilhelm E:\Excel files\130\m3a Sp06 130a solved.doc page 5 of 9 7) Wite down the diffeential equation fo a sping oscillating unde the influence of a i t damping foce bv. Use the following tial solution x() t = x0e ω and show how this leads to a quadatic equation fo the angula fequency ω. k=30n/m Assume a mass of.50 kg fo the sping. If it takes 45 seconds fo the amplitude of this sping to be educed fom 5.0 cm to.50 cm, find the value of the coefficient of fiction b. Calculate ω and ω 0. b=4.7e-; i 1 b b b ω = i ± ω = ± ω m m m ω = 3.46, ω = ) [10] In the Boh model of the hydogen atom, the electon moves in a cicula obit of adius 0.59E-10 m aound the poton. Assuming the angula momentum of the electon aound the nucleus is h/π, calculate the obital speed of the electon in electon Volts ev, and the angula fequency of the electon s motion. 1eV=1.60E-19J l=mv; v=.19e6m/s K=.19E-18J=13.6eV ω=4.14e16s -1
6 Physics: D. F. Wilhelm E:\Excel files\130\m3a Sp06 130a solved.doc page 6 of ) A sine wave is given by the function y( xt, ) = 5.00cm sin x t Calculate the m s powe equied to keep such wave moving on a sting if it is unde a tension T of.00n. v T = ; μ =8.E-3 kg/m μ powe=3.9w 10) [10] A sping with sping constant k=38.5 N/m and mass M=1.5 kg moves in simple hamonic motion with an amplitude of 5.0cm. When an exteio peiodic foce with magnitude.50 N and angula fequency 5.54 ad/s is applied fo a long time (so that the sping oscillates with the exteio diving fequency), find the new amplitude of the sping oscillation. Stat with the diffeential equation of the sping unde the influence of the exteio foce. Use as a tial solution the following function: xt ( ) = A cos ω t ; ω = angula fequency of the diving foce. ( f ) f ω0 = 30.8 Solve fo A. Show how to find it: F0 A = m ω0 ω f A=18.5m
7 Physics: D. F. Wilhelm E:\Excel files\130\m3a Sp06 130a solved.doc page 7 of 9 Optional: Descibe the double slit expeiment with light. Explain why the esults of this same expeiment with electons is so stange. What is the diffeence between the expeiment with electons and that with light. Fomulas: (1.1) L = dθ ω = dt (1.) p = mv = u d m( u dt dθ dt L=m ω = m ; k=u uθ + ωu θ ) = m ωk ) (1.3) N I = m dm fo the otation of objects with mass m o dm aound a fixed axis. (1.4) i= 1 i i total mass 1 K = I ω ; I = I + Md A A cm i (1.5) L= IAω
8 Physics: D. F. Wilhelm E:\Excel files\130\m3a Sp06 130a solved.doc page 8 of 9 af ) = bv( t) bx& damping bf ) = kx bx& = mx && o b b k k t m cx )&& + x& + x= 0; ω0 = ; xt ( ) = Ae cos( ω1t+ ϕ) m m m Hamonic motion with peiodic exteio foce: F cos ω t (1.6) (1.7) simple pendulum: ω (1.8) 0 ( f ) k F0 && x + x= cos ω f t { m m ω 0 ( ) g m = physical pendulum ω = g l I 0 0 iθ zˆ = Ae = A θ + i θ = a+ ib + b = zz ˆˆ θ = ( ) (cos sin ) ; with A= a actan ( ) ( ) k i θ+ nπ zˆ = e = a+ ib= cos θ + nπ + isin θ + nπ has k solutions: (1.9) 1 ( θ+ nπ) i ˆ k k z = e fo n=0,1...k-1 n A b a Powe in a vibating sting: 1 (1.10) = v μ Α ω Wave equation: (1.1) y = y sin( kx ωt) 0 (1.11) y t y x = v ω λ v= = = λ f k T FT (1.13) v = μ v B = ρ
9 Physics: D. F. Wilhelm E:\Excel files\130\m3a Sp06 130a solved.doc page 9 of 9
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