PHYS1303 - Special Relativity I

Assignment 1

Due date: 5:00pm, February 2, 2010

Give answers and explanations for the following questions.

1. (10 marks) What is the value of the gravitational acceleration on theEarth surface? With this acceleration, how long does it take to attainspeed of light, according to Newtonian mechanics?

2. (20 marks) Some student intended to measure the speed of sound bydoing the following. He connected a speaker far away with a longelectrical cable. He then measured the time difference between themoment he turned on the switch of the speaker and the moment heheard the sound. He concluded that the speed of sound is the distancefrom the speaker divided by the time difference. (a) Is this a good wayto measure the speed of sound? (b) Can we measure the speed of lightsimilarly by replacing the speaker by a flashlight?

3. (20 marks) In the lecture note, we take the approximation

1√

1 − β2≈ 1 +

β2

2. (1)

If we define the relative error as the difference of the two sides of theabove equation divided by the exact value, then what is the relativeerror for β = 0.01? How about β = 0.1 and β = 0.5?

4. (20 marks) Assume that Newtonian concept of space and time wascorrect. A train is traveling with speed 53m/s directly away from anobserver, Alice. (a) At time t = 0, the train is already 108m away fromher. What is the distance of the train from her when t = 15.2s? (b)Her watch, in fact, runs slower than an perfect clock by 20%, althoughshe has set her watch with the perfect clock at t = 0. What is thedistance of the train when her watch reads t′ = 15.2s? (c) What isthe speed of the train according to her? (d) Another observer, Bob, ison the train. His watch, unfortunately, synchronizes with Alice’s. Bobagrees to drop down from the train one apple each second. What is thedistance between apples?

5. (30 marks) (a) If we keep the β4 terms, what will Eq. (2.6) in the lecturenote become? (b) How about Eq. (2.10)?