### Answers and comments for the review activities and problems in Chapter 2.

#### GR

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): F_{1} = A/1. F_{2} = A/25. F_{1}/F_{2} = (A/1)/(A/25) = 25.

14. The ratio of weights is R_{E}^{2}/(R_{E} + 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 R_{E}^{2} + 2hR_{E} + h^{2} and neglect the last (tiny) term, so that the ratio becomes 1/(1 + 2h/R_{E}).

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/R_{E} which here is 1 - .0028. We see that the two weights differ by 0.28% or about 0.03N.

#### P&RSB

8. 1h

10. e.g. 1eV = 1.602 x 10^{-19}J

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.

#### SSP

4. The amounts were equal 6 x 10^{9}years ago.

5. q = 4.7 x 10^{-7}C