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PHYSICS: Princicple and Problem 2004

Paul W. Zitzewitz, Todd George Elliott, David G. Haase,Kathleen A. Harper

Chapter 1

A Physics Toolkit

Educators


Problem 1

For each problem, give the rewritten equation you would use and the answer.
A lightbulb with a resistance of 50.0 ohms is used in a circuit with a 9.0-volt battery.
What is the current through the bulb?

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Problem 2

For each problem, give the rewritten equation you would use and the answer.
An object with uniform acceleration a, starting from rest, will reach a speed of v in time t
according to the formula v=at. What is the acceleration of a bicyclist who accelerates
from rest to 7 m/s in 4 s?

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Problem 3

For each problem, give the rewritten equation you would use and the answer.
How long will it take a scooter accelerating at 0.400 $\mathrm{m} / \mathrm{s}^{2}$ to go from rest to a speed of 4.00 $\mathrm{m} / \mathrm{s} ?$

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Problem 4

For each problem, give the rewritten equation you would use and the answer.
The pressure on a surface is equal to the force divided by the area: $P=F / A . A 53-\mathrm{kg}$
woman exerts a force (weight) of 520 Newtons. If the pressure exerted on the floor is
$32,500 \mathrm{N} / \mathrm{m}^{2}$ , what is the area of the soles of her shoes?

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Problem 5

Use dimensional analysis to check your equation before multiplying.
How many megahertz is 750 kilohertz?

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Problem 6

Use dimensional analysis to check your equation before multiplying.
Convert 5021 centimeters to kilometers.

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Problem 7

Use dimensional analysis to check your equation before multiplying.
How many seconds are in a leap year?

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Problem 8

Use dimensional analysis to check your equation before multiplying.
Convert the speed 5.30 $\mathrm{m} / \mathrm{s}$ to $\mathrm{km} / \mathrm{h}$ .

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Problem 9

Solve the following problems.
a. $6.201 \mathrm{cm}+7.4 \mathrm{cm}+0.68 \mathrm{cm}+12.0 \mathrm{cm}$
b. $1.6 \mathrm{km}+1.62 \mathrm{m}+1200 \mathrm{cm}$

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Problem 10

Solve the following problems.
a. $10.8 \mathrm{g}-8.264 \mathrm{g}$
b. $4.75 \mathrm{m}-0.4168 \mathrm{m}$

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Problem 11

Solve the following problems.
a. $139 \mathrm{cm} \times 2.3 \mathrm{cm}$
b. $3.2145 \mathrm{km} \times 4.23 \mathrm{km}$

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Problem 12

Solve the following problems.
a. $13.78 \mathrm{g} \div 11.3 \mathrm{mL}$
b. $18.21 \mathrm{g} \div 4.4 \mathrm{cm}^{3}$

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Problem 13

Math Why are concepts in physics described with formulas?

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Problem 14

Magnetism The force of a magnetic field on a charged, moving particle is given by $F=B q v,$
where $F$ is the force in $\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}^{2}, q$ is the charge
in $\mathrm{A} \cdot \mathrm{s}$ , and $v$ is the speed in $\mathrm{m} / \mathrm{s}$ . $B$ is the strength of the magnetic in, measured in teslas, T. What is 1 tesla described in base units?

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Problem 15

Magnetism A proton with charge $1.60 \times 10^{-19} \mathrm{A} \cdot \mathrm{s}$
is moving at $2.4 \times 10^{5} \mathrm{m} / \mathrm{s}$ through a magnetic field
of 4.5 T. You want to find the force on the proton.
a. Substitute the values into the equation you will use. Are the units correct?
b. The values are written in scientific notation, $m \times 10^{n}$ . Calculate the $10^{n}$ part of the equation to estimate the size of the answer.
c. Calculate your answer. Check it against your estimate from part b.
d. Justify the number of significant digits in your answer.

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Problem 16

Magnetism Rewrite $F=B q v$ to find $v$ in terms of $F, q,$ and $B .$

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Problem 17

Critical Thinking An accepted value for the acceleration due to gravity is 9.801 $\mathrm{m} / \mathrm{s}^{2}$ . In an experiment with pendulums, you calculate that the value is 9.4 $\mathrm{m} / \mathrm{s}^{2}$ . Should the accepted value be tossed out to accommodate your new finding? Explain.

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Problem 18

Accuracy Some wooden rulers do not start with 0 at the edge, but have it set in a few millimeters.
How could this improve the accuracy of the ruler?

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Problem 19

Tools You find a micrometer (a tool used to measure objects to the nearest 0.01 mm) that has been
badly bent. How would it compare to a new, high-quality meterstick in terms of its precision? Its
accuracy?

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Problem 20

Parallax Does parallax affect the precision of a measurement that you make? Explain.

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Problem 21

Error Your friend tells you that his height is 182 cm. In your own words, explain the range of heights
implied by this statement.

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Problem 22

Precision A box has a length of 18.1 $\mathrm{cm}$ and a width of $19.2 \mathrm{cm},$ and it is 20.3 $\mathrm{cm}$ tall.
a. What is its volume?
b. How precise is the measure of length? Of volume?
c. How tall is a stack of 12 of these boxes?
d. How precise is the measure of the height of one box? of 12 boxes?

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Problem 23

Critical Thinking Your friend states in a report that the average time required to circle a $1.5-\mathrm{mi}$
track was 65.414 s. This was measured by timing 7 laps using a clock with a precision of 0.1 $\mathrm{s}$ . How much confidence do you have in the results of the report? Explain.

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Problem 24

The mass values of specified volumes of pure gold nuggets are given in Table $1-4$ .
a. Plot mass versus volume from the values given in the table and draw the curve that best fits all points.
b. Describe the resulting curve.
C. According to the graph, what type of relationship exists between the mass of the pure gold nuggets
d. What is the volume?
C. Write the equation showing mass as a function of volume for gold.
f. Write a word interpretation for the slope of the line.

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Problem 25

Make a Graph Graph the following data. Time is the independent variable.
$\begin{array}{|c|c|c|c|c|c|c|}\hline \text { Time (s) } & {0} & {5} & {10} & {15} & {20} & {25} & {30} & {35} \\ \hline \text { Speed ( } & {m / s)} & {12} & {10} & {8} & {6} & {4} & {2} & {2} & {2} \\ \hline\end{array}$

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Problem 26

Interpret a Graph What would be the meaning of a nonzero y-intercept to a graph of total mass versus volume?

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Problem 27

Predict Use the relation illustrated in Figure $1-16$ to determine the mass required to stretch the
spring $15 \mathrm{cm} .$

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Problem 28

Predict Use the relation in Figure $1-18$ to predict the current when the resistance is 16 ohms.

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Problem 29

Critical Thinking In your own words, explain the meaning of a shallower line, or a smaller slope
than the one in Figure $1-16,$ in the graph of stretch versus total mass for a different spring.

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Problem 30

Complete the following concept map using the following terms: hypothesis, graph, mathematical
model, dependent variable, measurement.

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Problem 31

Describe a scientific method.

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Problem 32

Why is mathematics important to science?

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Problem 33

What is the SI system?

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Problem 34

How are base units and derived units related?

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Problem 35

Suppose your lab partner recorded a measurement as 100 $\mathrm{g}$ . (1.1)
a. Why is it difficult to tell the number of significant digits in this measurement?
b. How can the number of significant digits in such a number be made clear?

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Problem 36

Give the name for each of the following multiples
of the meter. $(1.1)$
$\begin{array}{lll}{\text { a. } \frac{1}{100} \mathrm{m}} & {\text { b. } \frac{1}{1000} \mathrm{m}} & {\text { c. } 1000 \mathrm{m}}\end{array}$

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Problem 37

To convert 1.8 $\mathrm{h}$ to minutes, by what conversion
$\text { factor should you multiply? }$

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Problem 38

Solve each problem. Give the correct number of significant digits in the answers. (1.1)
a. $4.667 \times 10^{4} \mathrm{g}+3.02 \times 10^{5} \mathrm{g}$
b. $\left(1.70 \times 10^{2} \mathrm{J}\right) \div\left(5.922 \times 10^{-4} \mathrm{cm}^{3}\right)$

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Problem 39

What determines the precision of a measurement?

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Problem 40

How does the last digit differ from the other digits in a measurement?

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Problem 41

A car's odometer measures the distance from hon to school as 3.9 $\mathrm{km}$ . Using string on a map, you find the distance to be 4.2 $\mathrm{km}$ . Which answer do you think is more accurate? What does accurate mean? $(1.2)$

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Problem 42

How do you find the slope of a linear graph?

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Problem 43

For a driver, the time between seeing a stoplight and stepping on the brakes is called reaction time. The distance traveled during this time is the reaction distance. Reaction distance for a given driver and
vehicle depends linearly on speed. (1.3)
a. Would the graph of reaction distance versus speed have a positive or a negative slope?
b. A driver who is distracted has a longer reaction time than a driver who is not. Would the graph
of reaction distance versus speed for a distracted driver have a larger or smaller slope than for a
normal driver? Explain.

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Problem 44

During a laboratory experiment, the temperature of the gas in a balloon is varied and the volume of
the balloon is measured. Which quantity is the independent variable? Which quantity is the dependent variable?

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Problem 45

What type of relationship is shown in Figure 1-20? Give the general equation for this type of relation.

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Problem 46

Given the equation $F=m v^{2} / R,$ what relationship exists between each of the following? (1.3)
a. $F$ and $R$
b. $F$ and $m$
c. $F$ and $v$

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Problem 47

Figure $1-21$ gives the height above the ground of a ball that is thrown upward from the roof of a
building, for the first 1.5 s of its trajectory. What is the ball's height at $t=0 ?$ Predict the ball's height
at $t=2 \mathrm{s}$ and at $t=5 \mathrm{s}$ .

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Problem 48

Is a scientific method one set of clearly defined steps? Support your answer.

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Problem 49

Explain the difference between a scientific theory and a scientific law.

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Problem 50

Density The density of a substance is its mass per unit volume.
a. Give a possible metric unit for density.
b. Is the unit for density a base unit or a derived unit?

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Problem 51

What metric unit would you use to measure each of the following?
a. the width of your hand
b. the thickness of a book cover
c. the height of your classroom
d. the distance from your home to your classroom

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Problem 52

Size Make a chart of sizes of objects. Lengths should range from less than 1 mm to several kilometers.
Samples might include the size of a cell, the distance light travels in 1 s, and the height of a room.

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Problem 53

Time Make a chart of time intervals. Sample intervals might include the time between heartbeats, the time
between presidential elections, the average lifetime of a human, and the age of the United States. Find as
many very short and very long examples as you can.

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Problem 54

Speed of Light Two students measure the speed of light. One obtains $(3.001 \pm 0.001) \times 10^{8} \mathrm{m} / \mathrm{s}$ the other obtains $(2.999 \pm 0.006) \times 10^{8} \mathrm{m} / \mathrm{s}$
a. Which is more precise?
b. Which is more accurate? (You can find the speed
of light in the back of this textbook.)

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Problem 55

You measure the dimensions of a desk as $132 \mathrm{cm},$ $83 \mathrm{cm},$ and $76 \mathrm{cm} .$ The sum of these measures is $291 \mathrm{cm},$ while the product is $8.3 \times 10^{5} \mathrm{cm}^{3} .$ Explain how the significant digits were determined in each case.

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Problem 56

Money Suppose you receive $\$ 5.00$ at the beginning of a week and spend $\$ 1.00$ each day for lunch. You prepare a graph of the amount you have left at the end of each day for one week. Would the slope of
this graph be positive, zero, or negative? Why?

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Problem 57

Data are plotted on a graph, and the value on the $y$ -axis is the same for each value of the independent
variable. What is the slope? Why? How does $y$ depend on $x ?$

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Problem 58

Driving The graph of braking distance versus car speed is part of a parabola. Thus, the equation is
written $d=a v^{2}+b v+c$ . The distance, $d$ , has units in meters, and velocity, $v,$ has units in meters/ second. How could you find the units of $a, b,$ and $c ?$ What would they be?

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Problem 59

How long is the leaf in Figure 1-22? Include the
uncertainty in your measurement.

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Problem 60

The masses of two metal blocks are measured. Block $A$ has a mass of 8.45 g and block $B$ has a
mass of 45.87 g.
a. How many significant digits are expressed in these many significant digits are expressed in
these measurements?
b. What is the total mass of block A plus block B?
c. What is the number of significant digits for the total mass?
d. Why is the number of significant digits digits different for the total mass and the individual masses?

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