Chapter 1 ma | Physics homework help
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Chapter 01 Homework Assignment
Due: 11:59pm on Sunday, January 25, 2015
To understand how points are awarded, read the Grading Policy for this assignment.
Welcome!
Mastering presents homework items assigned by your instructor and works with you to answer them. Homework items
typically have an introduction, possibly figures, and one or more parts for you to answer.
Type of help offered
Mastering tells you immediately whether or not your answers are correct. Usually, you will have multiple
chances to arrive at the correct answer. Your instructor will determine how many tries you have available.
In many items, hints are available to help you if you get stuck. If you don’t need the hints to solve the
problem, you can still use them for review later on.
If you submit an incorrect answer, Mastering often responds with specific, helpful feedback.
Mastering is forgiving of many typos and formatting mistakes. If it can’t figure out what you entered, it will
let you know and give you another chance.
These exercises were chosen specifically to lead you through the key features of Mastering and are not intended to test
your knowledge of any specific subject material. Therefore, on this item you will not be penalized for using hints and
submitting incorrect answers. In fact, you should submit incorrect answers and use the hints to see what happens!
Part A
How many squares are in this grid ? Note that the
figure link lets you know that a figure goes along with this
part. This figure is available to the left.
Enter your answer as a number in the box below and
then submit your answer by clicking Submit.
ANSWER:
g
Number of squares = 5
Correct
What you are reading now is called a “followup
comment.” These comments typically offer more information or
provide an interpretation of the answer you just obtained.
Before you move on to a slightly more challenging question, have a quick look at the other buttons available
around the answer box.
Give Up allows you to complete the question if you can’t solve it on your own. Your instructor
controls whether or not the correct answer is displayed to you.
My Answers brings up a new window that lists all of the answers you have submitted for this
question, along with any helpful feedback you received for incorrect submissions.
Grading
See the help file available by clicking the Help link at the top right corner, if you want to know more about how grading
works in general. Here is the most important information you’ll need.
You must complete every part to get credit for an item. To complete a part, either answer the main part question correctly
or click the Give Up button.
In a graded homework item, each part counts equally toward your score on the overall item. If you get full credit on each
part, you will receive full credit for the problem. You may lose a fraction of the credit for a part when you submit an
incorrect answer. Whether you do lose credit and how much you lose are set by your instructor. However, you won’t lose
credit for most types of formatting mistakes or for submitting a blank answer.
As you might expect, you will receive no credit for a part if you use the Give Up button. If you just can’t figure out a
question, there is a way to get partial credit by using hints, as the following part will illustrate.
Part B
What is the magic number?
Note that there is a figure also associated with this part.
However, the figure for Part A may still be visible on the
left. To view the figure associated with Part B, click on the
figure link. A new figure should appear on the left.
You could try to guess the magic number but you
would probably use up all your tries before getting
the answer. Notice the new Hints button underneath
the answer box for this question. Clicking this button
will open up a list of hints that will guide you to the
correct number.
Hint 1. Different types of hints and their impact on grading
Notice that there are three hints for this question. You are not required to use all of the hints or to use them in
order. Each hint has a tagline that describes its contents. Based on the tagline you can decide whether or not
a particular hint will be useful to you.
There are two kinds of hints. Some hints, such as Hint 2 below, just provide you with information. Other hints,
such as Hint 3 below, give you an opportunity to answer a simpler question that is related to the main
question you are solving. These hints either have questions in the tagline or tell you to do something (e.g.,
Find…, Determine…, Identify…, etc.). There are two ways that this type of hint can help you:
Answering the simpler question gives you a chance to check that you are on the right track.
If you correctly answer the simpler question, you will receive partial credit for the part even if
you are unable to answer the main question.
Your instructor may choose to give you a bonus for not using hints or to deduct a small penalty for using
hints. If you are stuck, using the hints will usually result in a higher score than simply trying to guess because
you may lose fewer points for opening a hint than for getting the answer to the main question incorrect. There
is a more detailed explanation of how hints are graded in the help available by clicking the Help link at the top
right corner of your screen in the main Mastering window. In this problem, however, you will not lose any
credit for using the hints.
Now, open up the second hint for some help finding the magic number.
Hint 2. How to approach the problem
Although you could try to guess the magic number you would most likely exhaust your tries before getting the
correct answer. To help you, the magic number is , where is a number between 1 and 10.
Hint 3. What is ?
Recall that the previous hint stated that the magic number is , where is a number between 1 and
10. Specifically is an even number between 1 and 10. Try to guess the value of .
You may submit as many guesses as you need. Enter each guess into the answer box that follows.
ANSWER:
Correct
Now that you have determined , compute to find the magic number.
ANSWER:
Correct
Your instructor may choose to give you a bonus for not using hints or to deduct a small penalty for using hints.
If you are stuck, using the hints will usually result in a higher score than simply trying to guess because you
may lose fewer points for opening a hint than for getting the answer to the main question incorrect. Note that
you are never required to use the hints; if you want to figure the question out on your own, go ahead!
Notice that a new button, Review Part, appears when you correctly answer a part with hints. This button allows
you to review all of the hints for that part, even if you didn’t need them to get the answer. This is a useful way to
review the question when studying for a test. You do not lose any credit for reviewing the hints after you have
answered the question. If you didn’t look at all of the hints while answering the last question, you should read
through them now for some important information about hints and hint grading.
g4 4
4
g4 4
4 4
4 = 4
4 g
magic number = 60
Part C
Multiplechoice
questions have a special grading rule determined by your instructor. Assume that your instructor has
decided to grade these questions in the following way: If you submit an incorrect answer to a multiplechoice
question with options, you will lose of the credit for that question. Just like the similar multiplechoice
penalty on most standardized tests, this rule is necessary to prevent random guessing.
If a multiplechoice
question has five answer choices and you submit one wrong answer before getting the question
correct, how much credit will you lose for that part of the question?
ANSWER:
Correct
Your instructor may choose not to deduct of the credit for a multiplechoice
question with options.
To see how your instructor is grading you, click your instructor’s Grading Policy on your assignment page.
If you click on the Continue button before finishing all the Parts, you will see a message reminding you that you
need to complete each Part to get credit. If you have completed the item, clicking Continue will take you to the
next item on the Assignment. At any time you may click on the Provide Feedback link to access a survey page
without losing your work.
Once you have completed an item, you may access your score from the assignment. Your score will display
below the item title.
Significant Figures Conceptual Question
In the parts that follow select whether the number presented in statement A is greater than, less than, or equal to the
number presented in statement B. Be sure to follow all of the rules concerning significant figures.
Part A
Statement A: 2.567 , to two significant figures.
Statement B: 2.567 , to three significant figures.
Determine the correct relationship between the statements.
Hint 1. Rounding and significant figures
Rounding to a different number of significant figures changes a number. For example, consider the number
3.4536. This number has five significant figures. The following table illustrates the result of rounding this
number to different numbers of significant figures:
* *Ã
100
50
33
25
20
*Ã *
LN
LN
Four significant figures 3.454
Three significant figures 3.45
Two significant figures 3.5
One significant figure 3
Notice that, when rounding 3.4536 to one significant figure, since 0.4536 is less than 0.5, the result is 3, even
though if you first rounded to two significant figures (3.5), the result would be 4.
ANSWER:
Correct
Part B
Statement A: (2.567 + 3.146 ), to two significant figures.
Statement B: (2.567 , to two significant figures) + (3.146 , to two significant figures).
Determine the correct relationship between the statements.
ANSWER:
Correct
Evaluate statement A as follows: (2.567 + 3.146 ) = 5.713 to two significant figures is 5.7 .
Statement B evaluates as 2.6 + 3.1 = 5.7 . Therefore, the two statements are equal.
Part C
Statement A: Area of a rectangle with measured length = 2.536 and width = 1.4 .
Statement B: Area of a rectangle with measured length = 2.536 and width = 1.41 .
Since you are not told specific numbers of significant figures to round to, you must use the rules for multiplying
numbers while respecting significant figures. If you need a reminder, consult the hint.
Determine the correct relationship between the statements.
Statement A is
greater than
less than
equal to
Statement B.
LN LN
LN LN
Statement A is
greater than
less than
equal to
Statement B.
LN LN LN LN
LN LN LN
N N
N N
Hint 1. Significant figures and multiplication
When you multiply two numbers, the result should be rounded to the number of significant figures in the less
accurate of the two numbers. For instance, if you multiply 2.413 (four significant figures) times 3.81 (three
significant figures), the result should have three significant figures: . Similarly,
, when significant figures are respected (i.e., 15.328646 rounded to one significant
figure).
ANSWER:
Correct
Evaluate statement A as follows: (2.536 ) (1.4 ) = 3.5504 to two significant figures is 3.6 .
Statement B evaluates as (2.536 ) (1.41 ) = 3.57576 to three significant figures is 3.58 .
Therefore, statement A is greater than statement B.
Vector ComponentsReview
Learning Goal:
To introduce you to vectors and the use of sine and cosine for a triangle when resolving components.
Vectors are an important part of the language of science, mathematics, and engineering. They are used to discuss
multivariable calculus, electrical circuits with oscillating currents, stress and strain in structures and materials, and flows
of atmospheres and fluids, and they have many other applications. Resolving a vector into components is a precursor to
computing things with or about a vector quantity. Because position, velocity, acceleration, force, momentum, and angular
momentum are all vector quantities, resolving vectors into components is the most important skill required in a
mechanics course.
The figure shows the components of , and , along the x and y axes of the coordinate system, respectively. The
components of a vector depend on the coordinate system’s orientation, the key being the angle between the vector and
the coordinate axes, often designated .
g –
g –
Statement A is
greater than
less than
equal to
Statement B.
N N N N
N N N N
. 4 5
J
Part A
The figure shows the standard way of measuring the
angle. is measured to the vector from the x axis, and
counterclockwise is positive.
Express and in terms of the length of the
vector and the angle , with the components
separated by a comma.
ANSWER:
J
4 5
J
4 , 5 = DPTJ TJOJ
Correct
In principle, you can determine the components of any vector with these expressions. If lies in one of the
other quadrants of the plane, will be an angle larger than 90 degrees (or in radians) and and
will have the appropriate signs and values.
Unfortunately this way of representing , though mathematically correct, leads to equations that must be
simplified using trig identities such as
and
.
These must be used to reduce all trig functions present in your equations to either or . Unless
you perform this followup step flawlessly, you will fail to recoginze that
,
and your equations will not simplify so that you can progress further toward a solution. Therefore, it is best to
express all components in terms of either or , with between 0 and 90 degrees (or 0 and
in radians), and determine the signs of the trig functions by knowing in which quadrant the vector lies.
Part B
When you resolve a vector into components, the components must have the form or . The
signs depend on which quadrant the vector lies in, and there will be one component with and the other with
.
In real problems the optimal coordinate system is often rotated so that the x axis is not horizontal. Furthermore, most
vectors will not lie in the first quadrant. To assign the sine and cosine correctly for vectors at arbitrary angles, you
must figure out which angle is and then properly reorient the definitional triangle.
As an example, consider the vector shown in the diagram labeled “tilted axes,” where you know the angle
between and the y axis.
Which of the various ways of orienting the definitional
triangle must be used to resolve into components in
the tilted coordinate system shown? (In the figures, the
hypotenuse is orange, the side adjacent to is red, and
the side opposite is yellow.)
.
J R DPT J
TJO J
.
TJO È ] – ÃTJO ]
DPT È ] – ÃTJO ]
TJO ] DPT ]
TJO È ]DPT È Ã] –
TJO ] DPT ]] R
. ]]. DPT J ]]. TJO J
TJO J
DPT J
J
. J
.
.
J
Indicate the number of the figure with the correct orientation.
Hint 1. Recommended procedure for resolving a vector into components
First figure out the sines and cosines of , then figure out the signs from the quadrant the vector is in and
write in the signs.
Hint 2. Finding the trigonometric functions
Sine and cosine are defined according to the following convention, with the key lengths shown in green: The
hypotenuse has unit length, the side adjacent to has length , and the side opposite has length
. The colors are chosen to remind you that the vector sum of the two orthogonal sides is the vector
whose magnitude is the hypotenuse; red + yellow = orange.
J
J DPT J
TJO J
ANSWER:
Correct
Part C
Choose the correct procedure for determining the components of a vector in a given coordinate system from this list:
ANSWER:
Correct
Part D
The space around a coordinate system is conventionally divided into four numbered quadrants depending on the
1
2
3
4
Align the adjacent side of a right triangle with the vector and the hypotenuse along a coordinate direction
with as the included angle.
Align the hypotenuse of a right triangle with the vector and an adjacent side along a coordinate direction
with as the included angle.
Align the opposite side of a right triangle with the vector and the hypotenuse along a coordinate direction
with as the included angle.
Align the hypotenuse of a right triangle with the vector and the opposite side along a coordinate direction
with as the included angle.
J
J
J
J
signs of the x and y coordinates . Consider the following
conditions:
A. ,
B. ,
C. ,
D. ,
Which of these lettered conditions are true in which the
numbered quadrants shown in ?
Write the answer in the following way: If A were true in the third quadrant, B in the second, C in the first, and
D in the fourth, enter “3, 2, 1, 4” as your response.
ANSWER:
Correct
Part E
Now find the components and of in the tilted coordinate system of Part B.
Express your answer in terms of the length of the vector and the angle , with the components separated
by a comma.
ANSWER:
Correct
Exercise 1.12
4 5
4 5
4 5
4 5
1,4,2,3
4 5 .
J
4 , 5 = ÃTJOJDPTJ
Part A
The recommended daily allowance (RDA) of the trace metal magnesium is 410 for males. Express this
quantity in .
Express your answer using two significant figures.
ANSWER:
Correct
Part B
For adults, the RDA of the amino acid lysine is 12 per of body weight. How many grams per day should a 73
adult receive?
Express your answer using two significant figures.
ANSWER:
Correct
Part C
A typical multivitamin tablet can contain 2.0 of vitamin B2 (riboflavin), and the RDA is 0.0030 . How many
such tablets should a person take each day to get the proper amount of this vitamin, assuming that he gets none
from any other sources?
Express your answer as an integer.
ANSWER:
Correct
Part D
The RDA for the trace element selenium is 0.000070 . Express this dose in .
Express your answer using two significant figures.
ANSWER:
NHEBZ
NHEBZ
4.1×105 NHEBZ
NH LH
LH
0.88 HEBZ
NH HEBZ
2 tablets
HEBZ NHEBZ
Correct
Exercise 1.7
Part A
How many years older will you be 1.00 billion seconds from now? (Assume a 365day
year.)
ANSWER:
Correct
Exercise 1.24
You are using water to dilute small amounts of chemicals in the laboratory, drop by drop.
Part A
How many drops of water are in a 1.0 bottle? (Hint: Start by estimating the diameter of a drop of water.)
ANSWER:
Correct
± Vector Addition and Subtraction
In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their
components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem
gives you some practice with the components.
Let vectors , , and . Calculate the following, and express your answers as
7.0×10−2 NHEBZ
31.7 years
–
drops of water
drops of water
drops of water
drops of water
Õ
Õ
Õ
Õ
.- Ã .- Ã .-
ordered triplets of values separated by commas.
Part A
ANSWER:
Correct
Part B
ANSWER:
Correct
Part C
ANSWER:
Correct
Part D
ANSWER:
Correct
Part E
ANSWER:
.Ã. = 3,5,
4
.Ã. = 5,4,0
Ã..Ã. = 6,4,3
.Ã. = 3,
2,
11
Ã..Ã. = 11,14,8
Correct
Part F
ANSWER:
Correct
Tracking a Plane
A radar station, located at the origin of xz plane, as shown in the figure , detects an airplane coming straight at the station
from the east. At first observation (point A), the position of the
airplane relative to the origin is . The position vector
has a magnitude of 360 and is located at exactly 40
above the horizon. The airplane is tracked for
another 123 in the vertical eastwest
plane for 5.0 ,
until it has passed directly over the station and reached point
B. The position of point B relative to the origin is (the
magnitude of is 880 ). The contact points are shown in
the diagram, where the x axis represents the ground and the
positive z direction is upward.
Part A
Define the displacement of the airplane while the radar was tracking it: . What are the
components of ?
Express in meters as an ordered pair, separating the x and z components with a comma, to two
significant figures.
Hint 1. How to approach the problem
Keep in mind that .According to the rules of vector addition and subtraction, the x
component of is .
Hint 2. Finding the components of
.Ã .Ã. = 17,12,
6
.
.
N
EFHSFFT
EFHSFFT T
.
. N
. – Ã . .
.#”
.#”
. – Ã
.
.
.
#” – Ã .
4 .
4 .
4
.
. ? ?
What are the components of in the and directions?
Express your answer in meters as an ordered pair, separating the x and z values with commas, to
three significant figures.
ANSWER:
Hint 3. Finding the components of
What are the components of in the and directions?
Express your answer in meters as an ordered pair, separating the x and z components with a comma,
to three significant figures.
ANSWER:
ANSWER:
Correct
± Vector Dot Product
Let vectors , , and .
Calculate the following:
Part A
Hint 1. Remember the dot product equation
If and , then
.
ANSWER:
. % ? ‘?
4 , = 276,231 6 N
.
.
% ? ‘?
4 , = 842,257
6 N
. = 1100,26
#” N
.- Ã .- Ã .- ÃÃ
.- 4 5 6 .- 4 5 6
.ø.- 44 55 66
.ø . = 10
Correct
Part B
What is the angle between and ?
Express your answer using one significant figure.
Hint 1. Remember the definition of dot products
, where is the angle between and .
ANSWER:
Correct
Part C
ANSWER:
Correct
Part D
ANSWER:
Correct
Part E
Which of the following can be computed?
Hint 1. Dot product operator
The dot product operates only on two vectors. The dot product of a vector and a scalar is not defined.
J“# . .
.ø .- ].] ].] DPT JJ . .
J“# = 2 SBEJBOT
.ø . = 30
.ø . = 30
ANSWER:
Correct
and are different vectors with lengths and respectively. Find the following:
Part F
Express your answer in terms of
Hint 1. What is the angle between a vector and itself?
The angle between a vector and itself is 0.
Hint 2. Remember the definition of dot products
, where is the angle between and .
ANSWER:
Correct
Part G
If and are perpendicular,
Hint 1. What is the angle between perpendicular vectors?
The angle between vectors that are perpendicular is equal to radians or 90 degrees.
ANSWER:
.ø .ø .
.ø .ø .
.ø ..
ø .
.
.
.ø .- ].] ].] DPT JJ . .
= ø .
.
.
.
R
= ø .
.
Correct
Part H
If and are parallel,
Express your answer in terms of and .
Hint 1. What is the angle between parallel vectors?
The angle between vectors that are parallel is equal to 0.
ANSWER:
Correct
Finding the Cross Product
The figure shows two vectors and separated by an angle .
You are given that , , and
.
Part A
Express as an ordered triplet of values, separated by commas.
ANSWER:
.
.
= ø .
.
. . J56
.- .-
.g.- .
.
Correct
Part B
Find the magnitude of .
ANSWER:
Correct
Part C
Find the sine of the angle between and .
ANSWER:
Correct
Exercise 1.40
In each case, find the xand
ycomponents
of vector .
Part A
4.60 6.30
Enter your answers numerically separated by a comma. Express your answers using three significant
figures.
ANSWER:
Correct
.= 0,0,10
.
] ]. = 10
. .
TJO J = 0.707
.
– . Ã % ?
& ?
4 , 5 = 4.60,6.30
Part B
13.2 8.91
Enter your answers numerically separated by a comma. Express your answers using three significant
figures.
ANSWER:
Correct
Part C
15.0 22.4
Enter your answers numerically separated by a comma. Express your answers using three significant
figures.
ANSWER:
Correct
Part D
, where 4 6
Enter your answers numerically separated by a comma. Express your answers using one significant figure.
ANSWER:
Correct
Problem 1.81
While following a treasure map, you start at an old oak tree. You first walk 825 directly south, then turn and walk 1.25
at 30.0 west of north, and finally walk 1.00 at 40.0 north of east, where you find the treasure: a biography of
Isaac Newton!
Part A
To return to the old oak tree, in what direction should you head ? Use components to solve this problem.
– . Ã & ?
% ?
4 , 5 = 8.91,13.2
– Ã . % ?
& ?
4 , 5 = 15.0,22.4
– . ? – ? Ã % ?
& ?
4 , 5 = 20,30
N
LN È LN È
ANSWER:
Correct
Part B
To return to the old oak tree, how far will you walk? Use components to solve this problem.
ANSWER:
Correct
Score Summary:
Your score on this assignment is 63.1%.
You received 6.94 out of a possible total of 11 points.
= 8.90 J È west of south
= 911 N
