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# Physics for Scientists and Engineers I (GT PH 141

CSU

GPA 3.64

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This 19 page Class Notes was uploaded by Giovanna Yost on Tuesday September 22, 2015. The Class Notes belongs to PH 141 at Colorado State University taught by Carl Patton in Fall. Since its upload, it has received 45 views. For similar materials see /class/210312/ph-141-colorado-state-university in Physics 2 at Colorado State University.

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Date Created: 09/22/15

Page 1 Problems from Tipler and Mosca Physics for Scientists and Engineers 6th Edition Vol 1 Note These assignments are not to be turned in or graded Solution guides not solutions will be posted nominally on the target completion date These problems and their solutions will form the major basis for the construction of the objective multiple choice questions on the interm examinations and the nal examination Always strive to parameterize and not simply number crunch If the stated problem uses only numbers it is often more productive to assign parameters and work out the math The focus is not on number crunching and numerical answers but on indepth analysis and understanding In some instances an assigned problem will be commented sometimes extensively as an aid to the student in developing problem solving techniques Some individual problem solution guides will be more detailed and more speci c than others Some will be qualitative and some will give you a heavy dose of math All of it is to help you develop your own problem solving techniques and analytical approaches approaches that work for you Always diagram the problem yourself and make it as accurate as possible without overdoing it Solution Guide follows at the end of the problem list initial comments modi cations and hints below Assignment 11 31 October 2011 Target completion date 07 November 2011 TM11 1 11 80 2 14 65 3 14 104 4 15 01 5 15 36 6 15 37 7 15 87 8 15 90 Initial modi cations and comments and hints 1 11 80 Gravity integration problem Spherical symmetric mass with total mass M and a radius R but with a variable volume density pkgm3 C r What happens at r 0 Use a dm 47rpr2dr why Calculate the total mass set it equal to M and solve for C For the gravitational field gr determine the total mass inside some radius r0 and then use the law of universal gravity 2 14 65 You know that the acceleration of the cart plus pendulum down the incline is equal to g sin 9 This means there is an effective gravity as seen by the pendulum up the incline equal to g sin 9 This is in addition to the regular gravity straight down You get the total effective gravity by adding these vectors Hint draw a good diagram and obtain gm in terms of the vertical and horizontal components 3 14 104 If you did the original tunnel through the earth problem in Ch 11 TM9 10 ll 79 7 or you can revisit it now 7 you will realize that the force in toward the middle of the tunnel Page 2 always scales linearly with the distance from that center point call this distance x This is true no matter whether the tunnel goes through the center of the earth or takes some shorter path as in Fig 1438 This means that any mass in such a tunnel experiences harmonic motion Your quotF kxquot coefficient in TM9 10 is now our spring constant You should be able to take it from here and show that the period of oscillation or half period is only a function of the radius and mass of the earth and the gravitational constant G This means that if a person jumped into such a tunnel at one point on the surface he she would reach the other side in about 07 hours This could easily put airlines out of business 4 15 01 Make this quantitative What is the tension in a hanging rope as a function of the distance from the hang point for a rope of linear density 1 Do it for a real rope Make a decent estimate as to the linear density of the rope How much does a 50 foot long rope weigh 5 15 36 This is a very important principle It may seem strange at first to realize that ANY function of x Vt satisfies the 1D wave equation ANY function Try it for the functions provided Then prove it in general for some unspecified y f x Vt All you need to do is use the chain rule for taking derivatives over and over again 6 15 37 Another very important problem as preparation for standing waves in Ch 16 Visualize y Asinkxcos at as a function oftime at x 0 as a function of x at t 0 Then do it vs 1 at xl4l23l4 and A Then do it vs x at tT4T23T4 and T Why do you think this is called a standing wave 7 15 87 Classic Doppler effect problem with an additional small twist How far did the pulse travel and what is its speed We will discuss a more intuitive approach to the Doppler effect in class See ifthese equations make sense to you Sending The speeding car reduces Vsound Vcar squeezes the wavelength lair Eq 1 Traveling In air the sound travels at am vwmd The frequency is therefore given by rmr f mr vwmd Vsound Vsound f lair Vsound Vcar the car Tamar we have rmr awarvwr mervmmd Eq 2 car going one way and sound lair Vcar Vsound fhom As the re ected sound reaches the car for a period heard at going the other distance velocity times time which gives mg and l M Comb1n1ng we get fatal M fhom The main Tamar lair Vsound Vcar problem with the text is in the notation and remembering which is which The physical equations are Eqs 1 and 2 fatcar 8 15 90 Do this in parameters as well as numbers and visualize in parameters too The 2 function f x is a peaked function 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