1. You are
writing an adventure novel in which the hero escapes across the border with a
billion dollars’ worth of gold
in his suitcase. Could anyone carry that
much gold? Would it fit in a suitcase?
2. A
cross-country skier skis 1.00 km north and then 2.00 km east on a horizontal
snowfield. How far and in what
direction is she fromthe starting point?
3. After an
airplane takes off, it travels 10.4 km west, 8.7 km north, and 2.1 km up. How
far is it from the takeoff point?
4. How many
correct experiments do we need to disprove a theory?How many do we need to
prove a theory? Explain.
5. A guidebook
describes the rate of climb of a mountain trail as 120 meters per kilometer.
How can you express this
as a number with no units?
6. Suppose you
are asked to compute the tangent of 5.00 meters.Is this possible? Why or why
not?
7. A highway
contractor stated that in building a bridge deck he poured 250 yards of
concrete. What do you think he
meant?
8. What is your
height in centimeters? What is your weight in newtons?
9. What
physical phenomena (other than a pendulum or cesium clock) could you use to
define a time standard?
10. Describe
how you could measure the thickness of a sheet of paper with an ordinary ruler.
11. What are
the units of volume? Suppose another student tellsyou that a cylinder of radius
r and height h has
volume given by
r 3h.
Explain why this cannot be right.
r 3h.
Explain why this cannot be right.
12 Three
archers each fire four arrows at a target. Joe’s fourarrows hit at points 10 cm
above, 10 cm below, 10 cm to
the left,and 10 cm to the right of the
center of the target. All four of Moe’s arrows hit within 1 cm of a point 20 cm
from the center, and Flo’s four arrows all
hit within 1 cm of the center. The contest judge says that one of the
archers is precise but not accurate,another
archer is accurate but not precise, and the third archer is both accurate
and precise. Which description goes with
whicharcher? Explain your reasoning.
13. A circular
racetrack has a radius of 500 m. What is the displacement of a bicyclist when
she travels around the
track from the north side to the south side?
When she makes one complete circle around the track? Explain your
reasoning.
14. Can you
find two vectors with different lengths that have a vector sum of zero? What
length restrictions are
required for three vectors to have a
vector sum of zero? Explain your reasoning.
15. One
sometimes speaks of the “direction of time,” evolving from past to future. Does
this mean that time is a vector
quantity?Explain your reasoning.
16. Air traffic
controllers give instructions to airline pilots telling them in which direction
they are to fly. These
instructions are called “vectors.” If these
are the only instructions given, is the name “vector” used correctly? Why
or why not?
17. Can you
find a vector quantity that has a magnitude of zero but components that are
different from zero? Explain.
Can themagnitude of a vector be less than
the magnitude of any of its components? Explain.
18. (a) Does it
make sense to say that a vector is negative?
Why? (b) Does it make sense to say that one vector is
the negative of another? Why? Does your
answer here contradict what you said in part (a)?
19. How many
nanoseconds does it take light to travel 1.00 ft in vacuum? (This result is a
useful quantity to
remember.)
20. How many
years older will you be 1.00 gigasecond from
now? (Assume a 365-day year.)
21.With a
wooden ruler you measure the length of a rectangular piece of sheet metal to be
12 mm. You use micrometer calipers to measure the width of the rectangle and
obtain the value 5.98mm. Give your answers to the following questions to the
correct number of significant figures. (a) What is the area of the rectangle? (b)
What is the ratio of the rectangle’s width to its length? (c) What is the
perimeter of the rectangle? (d) What is the difference
between the
length and width? (e) What is the ratio of the length to the width?
