P-Chem II Course HWK 1 Solutions

P-Chem II Course HWK 1 Solutions - CHM4411—02...

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Unformatted text preview: CHM4411—02 [Phys—Chem. 11], Spring 2012 Instructor: H. Mattoussi 5“ a it Your name: —————— “j'j'sri‘“ 4-4;; Exercise 1 (5 points) A classical harmonic oscillator can be described by an ideal spring (with a spring constant k) to which end is attached a mass m. When the mass is moved from its resting position (defined as x=0) to a distance A, then released, it experiences a sustained oscillating motion. 1. Write the fundamental equation of movement. (the friction against the support surface are negligible) ,9 a» ’E% g, “T10 res F57W6€ «a 1" (Zia ft 1 f, (j/‘fiflx 14. {3;} i / *3 5‘5:er 2. Find the expression for the displacement x(t) as o; A; E? t ' 5 HM" Meg gist “" ‘5‘ ‘ 1 i. are, i g i I lgyg ’1 if A at i . .951: _ 5r a» day) 45:35,; 5’ ' m it éxv’ 5 "4%)? V" t £5 "5?" " ‘ E? ’32:? f a. V ’ l” .l’ \(fl W , a f) if a J a 3. Find the expression for the p(t) g: fie; :— Hi“ ) ,.: raft i363; s 5 43.53“ 4. Show that the total energy, Em = Ekin + Epot, (defined as the sum of the kinetic and potential energies) is constant. / I ‘ 2 C (‘J‘i as? if v fig. :1?" 3st .2: ,1: gf" 70/5171) 3; g, 0 Mac jg 2d .. .~ 5 1 “'°‘ L a“ P i F112, » t a» a; 2"" 52:? - I mi? 5a) éafiéfil‘i‘tz "r, n ‘a f t M =- m 1 Z 3%? Z ’2 \ ,9 'g Q 1;; r” I” it i“: Z 6 mt an; é: L‘Vflfi‘it 7 i I g a a: a. 3 5 t ” a?” e ' at? i 3 5 u: “awe g a 2 ix» ,\ / Exercise 2 (5 points) 1) If a force, F , is applied to an object of mass m (initially at rest), What happens to that object? 9* $53 “ ' ' ‘ i a it? 2) If the force is applied for a given time, 1;, what speed will the object gain (final speed) after the force is removed? W g?) c,“ a». 3:: 21> git; : hgre if) f t” i. "f: M» W” :35?” Wt Va 4) Practical example: an apple falling of a tree: The initial height of the apple is h, its mass m 3 300 mg. Express the force acting on the mass m‘ TATTM/“W vvvv tin“ , /,., .Vmwnwws -” Calculate the speed of the apple when it reaches the ground if the initial height was: 201m (AM; I " ‘ - r 1/ ”‘ (Q) “a! ;: c) 5m Exercice 3 (5 points) The angular momentum of a mass m orbiting around the center 0 is given by: J = rxp (vector product). This angular momentum can be expressed (for small size object) as: I]! = In). 1) What do I and to designate? Z : mmmi if W 5 “Vigefiele ’%’£%4aafi,wi, 2) Find a simple expression for l. 323:? V} E "a l g 1% 7‘92“! As done above for the linear motion in exercise 2, to accelerate the mass a torque T is applied to the mass. 3) Write the fundamental equation for this rotation motion: may) , , i 4) What will be the angular momentum of the mass be if the torque T is applied for given time 2' (we need an expression)? Rm»? was“ Exercice 4 (7.2.) (5 points) Explain why Planck’s introduction of quantized energy accounted for the properties of black body radiation. :75? i" [Sac/ray: ; LO gWVMQ/fiw amm doll,as¢m; K2! NW7LS‘1’? Cs [5w 9/ mgfiw- M 01V :’ I: J" 7’" i :1) Q’s/.1“ng and 1/(23): jZ+Vl$©/) Z 5—94”; My, it’lmz, ficeQ/e/J fi‘f M2, A V6494 file, jam/1A, V(o)::o MO {V}! ha}. QFCoCL. 1 We an Ac ZAML an 6970. fiv Z 7 mall/12¢ {ya} .5.) oi}:- as. Qf+€f§ 4/» all” wwm (“)S/Ijh (Anni 4/C M; 47/12 Ivan/‘0) flaw», ,2. :D %5@ ~ ~ij+k(tso) L W——-—* 1g 14, .51) “C;- 2" 2‘ ...
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P-Chem II Course HWK 1 Solutions - CHM4411—02...

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