EWR. third exam (Relativity)

Transcription

1 EWR third exam (Relativity) April 21, 2016, 19:00-21:00 Duration of the exam is 120 minutes The exam was made by W. Ubachs (VU) and peer-reviewed by A.-P. Colijn (UvA) Student name On the following page, you will find important information about the examination. Before starting with the examination you should read this information.

2 INSTRUCTION 1. This exam consists of 5 exercises. 2. You are allowed to use pens, and a calculator it is not allowed to program the calculator with programs intended specifically for this exam, or store equations in it. 3. Please write your name and student number on the front page of the exam before you answer the questions. 4. Please, write your answers on the given sheets. Write in readable script and provide some textual explanations as to why use equations. 5. You are not allowed to leave the examination room during the first 15 minutes of the examination and during the final half hour of the exam. 6. Please switch off any electronic devices and put them in your bag. Your bag needs to be closed. 7. Any violation of AUC s rules on fraud may lead to sanctions, ultimately to the exclusion of all examinations for one year (AS&P appendix 2, Regulations governing fraud and plagiarism). 8. Your grade will be calculated as the percentage of total points scored. The number of points per question is specified in the table below. 9. You are invited to inspect the grading of your exam within max 14 days from the day of the exam; you can make an appointment for that to meet lecturer at ARCNL at Science Park campus (w.ubachs@arcnl.nl). question a b c d e total Total 100

3 Equation sheet

4 1) Answer in short the following questions A) Why is it impossible to accelerate particles with non-zero rest mass to the speed of light? B) Mass-less particles such as photons (particles of light) that move outward from a gravitational field (potential) must loose energy. Will they be decelerated? How do they loose their energy?

5 2) A farm girl believes that she can fit a 12m long pole into a 10m long barn of she runs fast enough carrying the pole. A) Is this possible when considered by herself while running along (in her own frame of reference)? B) Is this possible for an observer standing next to the barn? For both cases A) and B) explain why or why not and under what conditions it would be possible.

6 3) Consider a moving stick of length L (in the reference system of the moving stick) as drawn in the figure below. L v θ The stick moves at an angle θ (such as depicted) at velocity v with respect to an observer. A) Derive a formula for the length of the stick, L in the reference system of the observer. (Hint: use projections L x and L y). B) Derive a formula for the angle θ in the system of the observer.

7 4) Addition of velocities A velocity transformation can be derived with u x the velocity in frame S and u x the velocity in frame S moving with constant velocity v with respect to S. A) Start out from the coordinate transformations given on the Equation sheet (36.6) and derive the velocity transformation, using Use: dx dx' u x = u x ' = dt dt' Derive: u x ux' + v = vu ' 1 + x 2 c B) Apply this: A first rocket moves at velocity 0.7c with respect to Earth. A second rocket moves at velocity 0.8c with respect to the first (along the same line). What is the velocity of the second rocket with respect to Earth?

8 5) Energy and mass in a bound system The hydrogen atom is composed of two particles, a proton which has mass M p= x kg or in units of MeV/c 2, and an electron of mass m e= x kg or MeV/c 2. When the hydrogen atom is formed (as a composite neutral particle) in its ground state its binding energy is 13.6 ev. A) What can you say about the mass of the hydrogen atom? Heavier or lighter than the sum of masses M p and m e? Explain in short. Quantum physics will teach us that the hydrogen atom can be in an excited state. Its first excited state is 10 ev higher than the ground state so, it has a binding energy of only 3.6 ev. B) What can you say about the mass of this excited hydrogen atom? Heavier or lighter than the atom in its ground state?

9 Extra sheet

10 Extra sheet