6. 0.8706, four.
7. Last one: A 2000C/day diet corresponds to an energy use of 97 J/s or 97 watts.
8. It decreases by a factor of 25.
Note: do not guess, but do it in detail (and you will be able to do more complicated examples easily): F1 = A/1. F2 = A/25. F1/F2 = (A/1)/(A/25) = 25.
14. The ratio of weights is RE2/(RE + h)2. The numerator and denominator are close and it's not a good idea just to use a lot of numbers on the calculator to do this with the necessary accuracy. We don't show you how to do this properly until page 250! Let's try it here:
Expand the denominator to RE2 + 2hRE + h2 and neglect the last (tiny) term, so that the ratio becomes 1/(1 + 2h/RE).
The binomial theorem (yes, that's what's on page 250), says that when x is much smaller than 1, (1 + x)-1 = 1 - x ..., so that the ratio becomes 1 - 2h/RE which here is 1 - .0028. We see that the two weights differ by 0.28% or about 0.03N.
10. e.g. 1eV = 1.602 x 10-19J
14. The sun's pull is greater by a factor of 178.
16. (22/19)2 = 1.34
18. Because Stiles would have had to be running with over 200 pounds of gold.
4. The amounts were equal 6 x 109years ago.
5. q = 4.7 x 10-7C