33

Homework Problems

1. Correct use of a calculator: (a) Calculate

74658

53222+97554

on a calcula-

tor.

[Self-check: The most common mistake results in 97555.40.]

(b) Which would be more like the price of a TV, and which would be more

like the price of a house, $ 3.5x10

5

or $ 3.5

5

.

2. Compute the following things. If they don't make sense because of units,

say so.

(a) 3 cm + 5 cm(b) 1.11 m + 22 cm

(c) 120 miles + 2.0 hours(d) 120 miles / 2.0 hours

3. Your backyard has brick walls on both ends. You measure a distance of

23.4 m from the inside of one wall to the inside of the other. Each wall is

29.4 cm thick. How far is it from the outside of one wall to the outside of

the other. Pay attention to significant figures.

4 . The speed of light is 3.0x10

8

m/s. Convert this to furlongs per fort-

night. A furlong is 220 yards, and a fortnight is 14 days. An inch is 2.54

cm.

5 . Express each of the following quantities in micrograms: (a) 10 mg, (b)

10

4

g, (c) 10 kg, (d) 100x10

3

g, (e) 1000 ng.

6 S. Convert 134 mg to units of kg, writing your answer in scientific

notation.

7. In the last century, the average age of the onset of puberty for girls has

decreased by several years. Urban folklore has it that this is because of

hormones fed to beef cattle, but it is more likely to be because modern girls

have more body fat on the average and possibly because of estrogen-

mimicking chemicals in the environment from the breakdown of pesticides.

A hamburger from a hormone-implanted steer has about 0.2 ng of estrogen

(about double the amount of natural beef). A serving of peas contains about

300 ng of estrogen. An adult woman produces about 0.5 mg of estrogen per

day (note the different unit!). (a) How many hamburgers would a girl have

to eat in one day to consume as much estrogen as an adult woman’s daily

production. (b) How many servings of peas.

8 S. The usual definition of the mean (average) of two numbers a and b is

(a+b)/2. This is called the arithmetic mean. The geometric mean, however,

is defined as (ab)

1/2

. For the sake of definiteness, let’s say both numbers have

units of mass. (a) Compute the arithmetic mean of two numbers that have

units of grams. Then convert the numbers to units of kilograms and

recompute their mean. Is the answer consistent. (b) Do the same for the

geometric mean. (c) If a and b both have units of grams, what should we

call the units of ab. Does your answer make sense when you take the square

root. (d) Suppose someone proposes to you a third kind of mean, called the

superduper mean, defined as (ab)

1/3

. Is this reasonable.

SA solution is given in the back of the book.A difficult problem.

A computerized answer check is available.

.

A problem that requires calculus.

Homework Problems