Tips for problem set 5

-For question 1, good warm-up problems are questions 3 and 2 from the tutorial (see the posted solutions to check whether you did it right)

-For question 2, warm up by looking at the solutions to questions 2 and 3 from Homework 4. There is one important difference:
           
For light or anything with m=0, we can't use E = gamma*m*c^2 or p = gamma * m * v since gamma is infinite (for v=c). Instead of thinking of energy and momentum as being determined by velocity, we can think of momentum as being the basic variable, and use the fact that energy is related to this by E = |p| c (we get this by plugging m=0 into the general relation E^2 = p^2 c^2 + m^2 c^4 and taking the square root).

You can also do this simple warm-up question. (solution provided on the second page)

-For question 3, you may wish to look back at some examples in your first-year physics text about circular motion and orbits in a gravitational potential. In part d, the idea is that P tells you how much energy the electon is losing per unit time, and since you already figured out how energy and radius are related, you should be able to figure out how much the radius changes per unit time.

-For question 4, the fourth question from the tutorial (and the basic discussion of intensity in the class notes) should be useful

In all questions where kinetic energy and momentum are involved, you need to decide whether to use the ordinary formula or the relativistic formula. If the speed in question is significantly less than the speed of light, the ordinary formula will give a good approximation (and it would just be needless work to use the relativistic one).