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### Phys105_ps5_2009

Course: PHY 105, Fall 2009
School: Princeton
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Word Count: 382

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105 Physics Problem Set 5 Due: Thursday, October 22, 2009, 3 PM to 208 Jadwin. Reading: For the 3 weeks before midterm break; roughly 1 chapter per week: K&amp;K, chapters 6, 7, 9. Our rst midterm exam is Mon., Oct. 19, in class. The problems on this exam will be from the material in the rst 4 problem sets, and Chapters 1-4 of K&amp;K. Problem 1. The slingshot maneuver: In the inertial reference frame of...

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105 Physics Problem Set 5 Due: Thursday, October 22, 2009, 3 PM to 208 Jadwin. Reading: For the 3 weeks before midterm break; roughly 1 chapter per week: K&K, chapters 6, 7, 9. Our rst midterm exam is Mon., Oct. 19, in class. The problems on this exam will be from the material in the rst 4 problem sets, and Chapters 1-4 of K&K. Problem 1. The slingshot maneuver: In the inertial reference frame of the Sun, a planet is moving in a circular orbit about the Sun with speed v . A spacecraft of mass m approaches the planet, moving antiparallel to the planets motion with speed ui before it is accelerated by the planets gravity. The spacecraft then passes pretty close to the planet, remaining outside of its atmosphere so the encounter is elastic. After the spacecraft leaves the gravitational inuence of the planet, it is moving directly away from the Sun with a new speed uf . What is uf ? What is the energy gained by the spacecraft from the planet? (In the reference frame of the Sun.) Make the approximations of ignoring the Suns gravitational inuence and that the mass the of spacecraft is innitesimal compared to the planet. This trick and many variations on it are used to explore the solar system and beyond. A rocket has to get the spacecraft from Earth up to the Moons orbit, but after that the craft can go anywhere by stealing kinetic energy and momentum rst from the Moon and then from planets. Problem 2. K&K, problem 6.7. Problem 3. K&K, problem 6.29. The end of the string is fastened to a point on the outer surface of the axle, so after the string fully unwinds, the string moves over to the other side of the axle and winds back up, causing the Yo-Yo to ascend. For part b, dene the time interval during which the string is fully unwound and the Yo-Yo turns around as that during which the tension in the string deviates from the values obtained in part a. Problem 4. K&K, problem 6.36. Give the motion, rA (t) and rB (t), in 2D Cartesian coordinates in the lab frame, with the initial position of mA as the origin, the initial motion of mB directed along the positive x-axis, and the moment of release being t = 0. 1
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Princeton - PHY - 105
Physics 105 Problem Set 5Due: Thursday, October 29, 2009, 3 PM to 208 Jadwin.Reading: K&amp;K, sections 7.1-7.6, chapter 9. Chapter 9 has more than the usual density oftypos, some of which are listed on the website under Course Materials/Chapters.Although
Princeton - PHY - 105
Physics 105 Problem Set 7Due: Thursday, November 12, 2009, 3 PM to 208 Jadwin.Reading: Chapter 9. Chapter 9 has more than the usual density of typos, some of whichare listed on the website under Course Materials/Chapters of K&amp;K. We will cover chapter1
Princeton - PHY - 105
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Princeton - PHY - 105
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Princeton - PHY - 105
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Princeton - PHY - 105
Physics 105, Problem Set 11Due: Friday, December 18, 2009, 3 PM.Reading: K&amp;K Chapters 11, 12, 13 with particular emphasis on 11.3-11.5, 12, 13.1-13.3.Knights Chapter 36 (on E-reserves on PHY103 website) contains additional discussion ofrelativity.Pro
Princeton - PHY - 105
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Princeton - PHY - 105
Physics 103H/105 Problem Set 1 SolutionsProblem 1 (3pts)Let a and b are unit vectors in the x-y plane making angles and with the x-axis respectively. is theiyaj()bixunit vector in the x direction and is the unit vector in the y direction.j(a)
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Princeton - PHY - 105
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Princeton - PHY - 105
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Princeton - PHY - 105
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Princeton - PHY - 105
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Princeton - PHY - 105
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Princeton - PHY - 105
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Princeton - PHY - 105
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Princeton - PHY - 105
Physics 105 Problem Set 10 SolutionsProblem 1 (4 pts)1. (Fermi 10.1) Calculate the work done in isobaric expansion.VfW=pdVVip = 2.34 atm = 2.37 105 N/m2 , Vi = 3.12 litres = 3.12 103 m3 , Vf = 4.01 litres = 4.01 103 m3 ;W = P (Vf Vi ) = 211 J2. (
Princeton - PHY - 105
Physics 105 Problem Set 11 SolutionsProblem 1 (3 pts)(a) When bouncing o a wall perpendicular to the x-axis, only the x-component of the atoms velocitychanges its sign. Collisions with the other walls do not aect the x-component of the atoms velocity.
Princeton - PHY - 105
Physics 105 Problem Set 12 SolutionsEach problem is worth 3 pointsProblem 9. 1 An observer sees two spaceships ying apart, each with speed 0.99c relative to the observer.What is the speed of one spaceship as viewed by the other?In order to solve the p
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