Physics 121 Hour Exam #5 60 Minutes, Take Home, Closed Book

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1 Physics 121 Hour Exam #5 60 Minutes, Take Home, Closed Book What s different about this exam? ˆ This is a 60-minute exam (like exams 1 through 3, but not like exam 4). The standard exam instructions: This exam is given under the Bryn Mawr honor code. Take it in a single sitting lasting no more than one and a half hours. This is a closed-book exam: do not use any references (text, notes, etc.). You will need a calculator capable of basic arithmetic and trigonometry, but you are not allowed to store formulas, etc., in the calculator memory, and if the calculator has built-in unit conversion functions, you are not allowed to use them. You may use a computer if it acts only as a calculator to do basic arithmetic. This exam covers topics from homework assignments 9 and 10, that is, material covered in class Friday, October 6, through Wednesday, November 18. You should know the material from earlier in the course, too, although that is not the focus of this exam. A sheet of formulas and constants covering course material to date is included in the exam. Copies of the formula sheet are available on the course website (and may be distributed in class) so that you can see their content ahead of time. You should use the copy of the formula stapled into the exam booklet when actually taking the exam. Return your exam in class on Monday, November 23. Do not discuss this exam with anyone until all the exams have been turned in. When you begin the exam, remove all the staples except the one in the upper left corner, and remove this first sheet and the equation sheet from the exam booklet. Write your answers directly on the exam booklet. Show your work and box your final answers. Partial credit is important! Always show your work! I can t give you credit if I don t know what you re thinking. In multi-part questions, if you get stuck on an early part, try to answer the later parts anyway either make up some answer for the early parts to use in the later parts, or describe what approach you would use to solve the later parts. Two blank pages are included at the end of the exam. If you need extra space to work a problem, use one of the end-pages, and put a note on the problem page indicating that you have done so. In any exam or assignment in this class, do not assume that you have to use every last piece of information given to solve a problem. Sometimes life gives you more information than you need. Good luck!!

2 Physics 121 Formulas and Constants, Page 1 of 2 1 (special relativity units) 299, 792, 458 m (exact) s Speed of light: c = (approximate) s 1.0 foot (approximate) ns Stefan-Boltzmann constant: σ = W m 2 K { Mass of electron m e = kg { MeV Mass of proton m p = kg 938 MeV Mass of Earth: m = kg Radius of Earth: r = m Mass of Sun: m = kg Radius of Sun: r = m Temperature of Sun: T = 5780 K Distance from Sun to Earth: 1 au = m Power output of Sun: L = W Grav. accel. at Earth surface: g = 9.8 m s 2 Density of water: ρ water = 1 g kg = 1000 cm3 m 3 f(x) f(x 0 ) + df dx (x 0)(x x 0 ) (1 + x) n 1 + nx p = m v K = 1 2 mv2 U = mgh P = E t v = x t I = P A I = P 4πr 2 T (Kelvins) = T ( C) P = eσat 4 s 2 = t 2 x 2 y 2 z 2 1 γ = 1 v 2 v = 1 1 γ 2 t = γ τ L = L R γ p = [γm, γmv x, γmv y, γmv z ] p = [E, p x, p y, p z ] m 2 = E 2 p 2 x p 2 y p 2 z m 2 = E 2 p 2 E = m + K E = γm E = γmc 2 E rest = m E rest = mc 2 E = p (special relativity units) (conventional units) (special relativity units) (conventional units) (light, special relativity units)

3 Physics 121 Formulas and Constants, Page 2 of 2 Lorentz transform : t = γ ( t + β x ) t = γ ( t β x) x = γ (+β t + x ) x = γ ( β t + x) y = y y = y z = z z = z Momentum transform : E = γ ( E + βp x) E = γ ( E βp x ) p x = γ (+βe + p x) p x = γ ( βe + p x ) p y = p y p z = p z p y = p y p z = p z Relativistic velocity transform : v x = β + v x 1 + βv x v y v y = γ(1 + βv x) v z v z = γ(1 + βv x) v x = β + v x 1 βv x v y v y = γ(1 βv x ) v z v z = γ(1 βv x ) Galilean velocity transform : v x = β + v x v x = β + v x v y = v y v y = v y v z = v z v z = v z 1 + v 1 v Relativistic Doppler shift : T R = 1 v T E f R = 1 + v f E v < 0 : emitter moving toward receiver v > 0 : emitter moving away from receiver v = ( ) 2 T R T E 1 ( ) 2 v = T R T E + 1 ( f E f R ) 2 1 ( f E f R ) 2 + 1

4 Physics 121 Hour Exam #5 Name Return this exam in class on Monday, November 23. This exam consists of a five problems on five pages. Point values are given with each problem. They add up to 99 points; you will get 1 free point to make a total of 100. In any given problem, points are not necessarily evenly divided between the parts. Two pages are supplied at the end of the booklet in case you need extra workspace. 1. [12 points] In a supernova explosion, the inner core of a star collapses while the outer layers of the star are blown away at high speed in all directions, as suggested by the drawing below. Centuries after such an explosion, the debris from the outer layer can still be seen to be flying away from the remaining core of the star. Before Explosion After Explosion Consider (i) the pre-explosion mass of the original star and (ii) the post-explosion mass consisting of the mass of the core that was left behind plus the mass of the debris that was blown away after the explosion. Which of these is greater, pre-explosion mass or post-explosion mass, or are they the same? Briefly justify your answer. 1

5 2. [12 points] Can a photon (particle of light) decay into a single particle which has mass (m > 0)? Briefly justify your answer. 2

6 3. [25 points] A particle with mass M 0 and speed 3 collides with a particle of mass 5 7 M 4 0 at rest. They coalesce to form a single new particle. What is the mass and speed of this new particle? 3

7 4. [25 points] A particle of initial mass m i moves in the +x direction at speed v i, corresponding to Lorenz factor γ i. A photon of energy E moves in the +y direction. The photon collides with the particle and is absorbed by it. (This is like two things hitting and sticking together, except one of those things is a photon of light). After absorbing the photon, the particle moves off at some angle θ, as shown. What is θ? (Your answer should be a formula which depends on E, m i, v i, and/or γ i,) Before Absorption After Absorption v f v i θ photon 4

8 5. [25 points] A spaceship is moving at speed v = 0.866, which corresponds to γ = 2, toward the Earth. A laser beam is emitted by the spaceship in the direction of Earth. The beam consists of photons each of which has energy E as measured in the spaceship reference frame. v=0.866 Earth (a) What is the energy of one of these photons in the Earth reference frame? (Your answer should be a formula which depends on E.) (b) In quantum mechanics, it is claimed that the frequency of a photon is proportional to its energy. This can be written E = hf, where E is the photon energy, f is its frequency, and h is a physical constant which is the same number for all photons. Consider the Doppler shift of the frequency of the a photon emitted in the spaceship reference frame and received in the Earth reference frame. Is your answer to (a) consistent with this Doppler shift? Justify your answer using formulas or a calculation. (Don t just answer yes or no ). 5

9 This is the first of two pages provided as extra work space for this exam. 6

10 This is the second of two pages provided as extra work space for this exam. 7

Physics 121 Hour Exam #1 60 Minutes, Take Home, Closed Book

Physics 121 Hour Exam #1 60 Minutes, Take Home, Closed Book This exam is given under the Bryn Mawr honor code. Take it in a single sitting lasting no more than one hour. This is a closed-book exam: do