EXAM 3 REVIEW: hardest problems

Transcription

1 PHYS 17: oern echanics Spring 011 xa 3 results: ultiple choice: 4.5/70 = 60.7% Hanwritten: XXX FINAL XA: 1. Coprehensie. About 0-5 ultiple choice questions only. If you hae Final xa conflict: 1. Notify us ieiately (before next onay, Apr 5). Inicate your exa scheule for Thursay, Friay an Saturay.. Depening on your input, the akeup exa will be scheule for Friay or Saturay. Lecture 5 ntropy ea XA 3 VIW: harest probles

2 xa 3: Harest proble, 39% A rocket is at rest (not oing) in outer space far away fro any assie objects, i.e. the external net force on the rocket is negligible. The rocket turns on its engine throwing out burning gases of rocket fuel to the left, while accelerating the right. Consier a syste consisting of the rocket, fuel an burning gases, an escribe the irection of otion of the center of ass of this syste. P net, ext 39% A) The center of ass will not oe 1% B) The center of ass will accelerate to the right at the sae rate as the rocket itself 44% C) The center of ass will accelerate to the right at rate that is saller than that of rocket 3% D) The center of ass will accelerate to the left 1% ) The answer epens on the cheical energy release uring burning What will be the elocity of the center of ass c? C = F LCTU 16 clicker question: A syste is ly at rest an consists of a an with a bottle sitting on ice (ignore friction). The an then throws the bottle away as shown. 3 xa 3: Harest proble, 39% A rocket is at rest (not oing) in outer space far away fro any assie objects, i.e. the external net force on the rocket is negligible. The rocket turns on its engine throwing out burning gases of rocket fuel to the left, while accelerating the right. Consier a syste consisting of the rocket, fuel an burning gases, an escribe the irection of otion of the center of ass of this syste. P net, ext 39% A) The center of ass will not oe 1% B) The center of ass will accelerate to the right at the sae rate as the rocket itself 44% C) The center of ass will accelerate to the right at rate that is saller than that of rocket 3% D) The center of ass will accelerate to the left 1% ) The answer epens on the cheical energy release uring burning C = F

3 xa 3: Har proble, 4% Two hockey pucks are pulle using attache weightless strings as shown using the sae force. The string in case is wrappe aroun the puck an can unwin freely. In case 1 it is attache to the center. Which puck will accelerate quicker? P C = F net, ext 4% A) They accelerate at the sae rate 46% B) Puck 1 10% C) Puck 1% D) ass of the puck is neee to answer this question 5 xa 3: Har proble, 4% A string is wrappe aroun a isk of ass = 1.6 kg an raius = Starting fro rest, you pull the string with a constant force F = 6 N along a nearly frictionless surface. At the instant when the center of the isk has oe a istance x = 0.10, a length = 0.8 of string has unwoun off the isk. 6% A) K rot = F. 13% B) K rot = F. x 1% C) K rot = F. + F. x 4% D) K rot = F. - F. x 6

4 xa 3: Har proble, 4% A sphere of ass is attache to a fixe piot by a weightless string. Initially, it oes aroun the circle of raius with spee. As it keeps circling the string is pulle into the sphere by a echanis hien within the sphere. What will be the linear spee f of the sphere when it gets two ties closer to the axle, i.e. oes aroun a circle of raius /? A) f = 4% B) f = 4 9 C) f = 10 D) f = / 1 ) f = /4 7 LA = ra F L = r p A A net LA = ra p ra = const 7 xa 3: Har proble, 55% A perfectly elastic ball of ass 100 g bounces off the arth. Which of the stateents are correct: 1) The elocity (ector) of the ball experiences larger change uring the collision than the elocity of arth A: TU B: FALS (not to scale) ) The oentu of the ball experiences larger change uring the collision than the oentu of arth A: TU B: FALS 3) The position of the center of ass of the syste ball+arth fluctuates in the process A: TU B: FALS 8

5 xa 3: Har proble, 58% A bullet of ass is fire horizontally an at a istance aboe the axis of a cyliner of ass, raius. The cyliner is ly at rest an is free to rotate surface as it hits it. The cyliner begins to rotate at an angular spee such that it copletes one coplete reolution in T after catching the bullet. Calculate the spee of the bullet prior to ipact. 1. Which funaental principle will you use? A) oentu principle B) nergy principle C) Angular oentu principle D) None of the aboe 9 xa 3: Har proble, 58% A bullet of ass is fire horizontally an at a istance aboe the axis of a cyliner of ass, raius. The cyliner is ly at rest an is free to rotate surface as it hits it. The cyliner begins to rotate at an angular spee such that it copletes one coplete reolution in T after catching the bullet. Calculate the spee of the bullet prior to ipact.. Angular oentu of which syste is consere uring collision? A) Bullet B) Cyliner LA = r C) Bullet + cyliner A Fnet =τ A D) None of the aboe Approxiation: all other interactions uring collision are negligible 10

6 xa 3: Har proble, 58% A bullet of ass is fire horizontally an at a istance aboe the axis of a cyliner of ass, raius. The cyliner is ly at rest an is free to rotate surface as it hits it. The cyliner begins to rotate at an angular spee such that it copletes one coplete reolution in T after catching the bullet. Calculate the spee of the bullet prior to ipact. Initial angular oentu in respect to center axle: A) B) C) D) L = + 0 L = + 0 L = + L = + / 11 xa 3: Har proble, 58% A bullet of ass is fire horizontally an at a istance aboe the axis of a cyliner of ass, raius. The cyliner is ly at rest an is free to rotate surface as it hits it. The cyliner begins to rotate at an angular spee such that it copletes one coplete reolution in T after catching the bullet. Calculate the spee of the bullet prior to ipact (I isk = /). L = What is the angular oentu? f = ω ω = π T L = ( + ) ω L = ω + f A) B) C) L = ω + f 1

7 xa 3: Har proble, 58% A bullet of ass is fire horizontally an at a istance aboe the axis of a cyliner of ass, raius. The cyliner is ly at rest an is free to rotate surface as it hits it. The cyliner begins to rotate at an angular spee such that it copletes one coplete reolution in T after catching the bullet. Calculate the spee of the bullet prior to ipact (I isk = /). f = ω ω = π T = ω + f π = + T Fin 13 The Boltzann istribution N=100 oscillators, q=4 quanta What is the probability to fin an ato in a soli at certain energy leel? Separate syste into objects: Object 1: 99 atos Object : 1ato Ω = ( q + N ) q! ( N 1 )! 1! Clicker: In how any ways can we istribute 4 quanta in object? A) 1 way B) 4 ways C) 4!=1**3*4=4 ways Total nuber of icrostates with n quanta in object : Ω = Ω1Ω = Ω1 Probability to fin n quanta on Object is proportional to the nuber of icrostates with (q-n) quanta in Object 1

8 The Boltzann istribution N=100 oscillators, q=4 quanta What is the probability to fin an ato in a soli at certain energy leel? The Boltzann istribution The probability of fining a icroscopic syste to be in a state with energy aboe groun state is proportional to Ω ( ) e kt For large systes! Boltzann factor Nuber of icrostates corresponing to energy See pages for eriation The Boltzann istribution e kt e -1 =0.37 Clicker: At ery high teperature it is possible to hae ore oscillators in the first excite state than in groun state. A) True B) False e -1 =0.37

9 The Boltzann istribution: hyrogen at T e kt oo teperature ~300 K: kt = 0.06 ev 10. ev kt=0.06 ev Teperature at which kt = 10. ev : T=10,000 K The Boltzann istribution easure energy on a single oscillator any ties. Nuber of easureents at energy is proportional to: e kt easure energy on each oscillator on a syste at once. Nuber of oscillators at energy is proportional to: e kt Boltzann istribution: istribution of oscillator energies in a large syste