Stuck on a few Physics 11 questions regarding the Theory of Special Relativity. Help would be awesome!?

Question

Here are the three questions I am having trouble answering from this portion of the course:

1) Let's assume for a moment that your house uses an average of 16 kwh of electrical energy per day. If you could convert the mass of a 46 g golf ball into electrical energy, how many years supply of energy would you have? (1 kWh = 3.6 x 10^6 J)

2) Suppose you're shining a light while riding on a train. When you shine the light in the direction the train is moving, how would the speed of light appear to an observer standing at rest outside the train? (Does it increase or appear the same as if the observer were riding on the train?)

3) If you were in a high-speed spaceship traveeling away from the aerth at a speed close to that of light, would you measure your normal pulse to be slower, the same or faster? How would your meaurements of pulses of friends back on Earth be if you could monitor them from your ship?

If you could give me a hand with any or all of these that would be so awesome. Thank you so much, I really appreciate it.

Answer 1

(1) use E = m*c^2 to get:

E = .046kg * (3*10^8 m/s)^2

E = 4.14*10^15 J

(2) The speed of light would be the same for an observer next to the train as on the train. However the frequency would change. When the train is coming toward the stationary observer the wave peaks would appear closer together when the train is moving away from he stationary observer the wave peaks would appear further apart. This is the cause of red and blue shift when we look at stars.

(3) On a near speed of light ship your pulse would remain the same according to your own measurements. However if you could measure the pulse rates of your friends back on earth they would be greatly increased. The Lorentz transforms give that time and space dilate at relativistic speeds so what seemed a short trip (lets say five minutes) to a nearby star system to you would be years to the people on earth.

Answer 2

For item #1, you're being asked to use E = mc^2.  You are given m (0.046 kg), and you should know c=speed of light =3e8m/s.  You should also know that 1 J = 1 kg m/s^2.  So you convert from mass, to energy in Joules, convert from Joules to kWh, then divide by 16 kwh per day -- which gives you days.

#2 and 3 -- the key points of special relativity are that:

   - speed of light is constant for all observers, regardless of their frame

   - laws of physics are the same for any observer in an inertial coordinate frame (non accelerating).

So ... if you're travelling at constant velocity, on a train or spaceship, any experiment you run on that train or spaceship will have the same result whether you are stationary or moving with respect to the earth.  Your rulers appear fine, your clocks appear to run correctly.

BUT, if you observe an experiment that is occuring in a frame moving with respect to you -- you think their clocks run slow, and their rulers are too short -- but you still both measure the same speed of light.

So in #2, speed of light is constant, regardless of observer.

In #3, you would not see any problem with your pulse, but you would think you're friend's pulse is slow, since he is moving with respect to you.  Your friend would think that your pulse is slow (since you seem to be moving with respect to him)!