Problem 1 A man, travelling on a ship, measures a time of 8.0 s occurring in a given instant. How would the relativistic time vary if the ship travelled at: a) 25 m/s b) 1500 m/s c) 0.5 c (half the speed of light) In this scenario, note Lm will always be less than L5, hence "length contraction\" Let's try a case! Problem 2 A man, travelling on a ship, measures a length of 500.0m occurring in a given instant. How would the relativistic length vary if the ship travelled at: a) 25 m/s b) 1500 m/s c) 0.5 c (half the speed of light) Einstein's Twin Paradox You've seen the effects of travelling near the speed of light, but that lead to a neat experiment called the twin paradox Insert page here Problem 3 We have a set of twin children: one on Earth, and the other on a ship travelling 8.6 light years away on a ship that is travelling at 0.90c. Once the voyage has ended, what do you expect will occur?Fact: the total daily energy consumption in Canada in 2008 was This is why scientists are aiming to use nuclear reactions to extract this rest energy However, the most efficient reactor only gets 1% of the rest energy Quick energy ugdote G) Our book often introduces a new form to measure energy, called the (derived from V=E/q) G) The conversion from joules to the electron volt is found below: 1 J: 6.242 x 1018 eV Or 1 eV= 1.6 x 1019] Problem 4 The average home in Canada uses 3.6 x1010] of energy per day. Imagine that a cabbage with a rest mass of 0.750 kg could be completely converted to another form of energy (although in a nuclear reaction only a fraction of the mass is converted into electrical energy). (a) Calculate how much energy is released by the cabbage. (b) Determine the number of days this cabbage could supply energy for an average home in Canada. **This can be used to define the relativistic time! Limitations of the formula From the formula above, what CANNOT happen ever? Explain why this is so. Hint.. Look below Atm Ats 2- 0- 0 0.2 0.4 0.6 0.8 1.0 V CvAt 2 2 = d'+ 2 Squaring z, 23 = c? ( At m ) 2 4 c2(At )2 = d2 + v2(At )2 multiply both by 4, divide by c2 4 4 (At ) ? = 4d2 2 2 ( 4t ) 2 move circled term to RS, factor 4d2 = divide factored bracket from RS to LS 4d2 ( Atm ) ? =vAt 2 2 = d'+ 2 Squaring z, 23 = c? ( At m ) 2 4 c2(At )2 = d2 + v2(At )2 multiply both by 4, divide by c2 4 4 (At ) ? = 4d2 2 2 ( 4t ) 2 move circled term to RS, factor 4d2 = divide factored bracket from RS to LS 4d2 ( Atm ) ? =