Chapter 01 Homework

3/3/2014 Chapter 1 Homework

http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2728901 1/15

Chapter 1 Homework

Due: 10:00pm on Friday, January 31, 2014

You will receive no credit for items you complete after the assignment is due. Grading Policy

Scientific Notation

A number written in scientific notation has the form , where and is an integer.

Part A

Consider the expression . Determine the values of and when the value of this expression is

written in scientific notation.

Enter and , separated by commas.

Hint 1. A walk-through

Express all the numbers in the expression using scientific notation. You should get a fraction of the form

,

or

To determine , you have to divide by . This will often give you something that is not between 1

and 10; thus you have to write it in scientific notation:

.

The next step is to find in the expression

Do this by subtracting and from :

.

The value of you are looking for is equal to , while is equal to .

ANSWER:

Correct

a × 10k 1 ≤ a < 10 k

18×10−6

(0.003)(12× )10−2 a k

a k

×a1 10k1

( × )( × )a2 10k2 a3 10k3

.a1⋅a2 a3

10k1

⋅10k2 10k3

a a1 ⋅a2 a3

= ×a1⋅a2 a3

a4 10k4

k5

= .10k5 10k1

⋅10k2 10k3

k2 k3 k1

= − ( + )k5 k1 k2 k3

a a4 k +k4 k5

, = 5,-2a k



Dimensions of Physical Quantities

Learning Goal:

To introduce the idea of physical dimensions and to learn how to find them.

Physical quantities are generally not purely numerical: They have a particular dimension or combination of dimensionsassociated with them. Thus, your height is not 74, but rather 74 inches, often expressed as 6 feet 2 inches. Althoughfeet and inches are different units they have the same dimension--length.

Part A

In classical mechanics there are three base dimensions. Length is one of them. What are the other two?

Hint 1. MKS system

The current system of units is called the International System (abbreviated SI from the French SystèmeInternational). In the past this system was called the mks system for its base units: meter, kilogram, andsecond. What are the dimensions of these quantities?

ANSWER:

Correct

There are three dimensions used in mechanics: length ( ), mass ( ), and time ( ). A combination of these threedimensions suffices to express any physical quantity, because when a new physical quantity is needed (e.g., velocity),it always obeys an equation that permits it to be expressed in terms of the units used for these three dimensions. Onethen derives a unit to measure the new physical quantity from that equation, and often its unit is given a special name.Such new dimensions are called derived dimensions and the units they are measured in are called derived units.

For example, area has derived dimensions . (Note that "dimensions of variable " is symbolized as .)

You can find these dimensions by looking at the formula for the area of a square , where is the length of a

side of the square. Clearly . Plugging this into the equation gives .

Part B

Find the dimensions of volume.

Express your answer as powers of length ( ), mass ( ), and time ( ).

acceleration and mass

acceleration and time

acceleration and charge

mass and time

mass and charge

time and charge

l m t

A [A] = l2 x [x]A = s2 s

[s] = l [A] = [s =]2 l2

[V ]

l m t



Hint 1. Equation for volume

You have likely learned many formulas for the volume of various shapes in geometry. Any of these equationswill give you the dimensions for volume. You can find the dimensions most easily from the volume of a cube

, where is the length of the edge of the cube.

ANSWER:

Correct

Part C

Find the dimensions of speed.


Hint 1. Equation for speed

Speed is defined in terms of distance and time as

.

Therefore, .

Hint 2. Familiar units for speed

You are probably accustomed to hearing speeds in miles per hour (or possibly kilometers per hour). Thinkabout the dimensions for miles and hours. If you divide the dimensions for miles by the dimensions for hours,you will have the dimensions for speed.

ANSWER:

Correct

The dimensions of a quantity are not changed by addition or subtraction of another quantity with the same dimensions.This means that , which comes from subtracting two speeds, has the same dimensions as speed.

It does not make physical sense to add or subtract two quanitites that have different dimensions, like length plus time.You can add quantities that have different units, like miles per hour and kilometers per hour, as long as you convert bothquantities to the same set of units before you actually compute the sum. You can use this rule to check your answersto any physics problem you work. If the answer involves the sum or difference of two quantities with different dimensions,then it must be incorrect.

V = e3 e

= [V ] l3

[v]

l m t

v d t

v = dt

[v] = [d]/[t]

= [v] lt

Δv



This rule also ensures that the dimensions of any physical quantity will never involve sums or differences of the basedimensions. (As in the preceeding example, is not a valid dimension for a physical quantitiy.) A valid dimension

will only involve the product or ratio of powers of the base dimensions (e.g. ).

Part D

Find the dimensions of acceleration.


Hint 1. Equation for acceleration

In physics, acceleration is defined as the change in velocity in a certain time. This is shown by the

equation . The is a symbol that means "the change in."

ANSWER:

Correct

Exercise 1.11

In the fall of 2002, a group of scientists at Los Alamos National Laboratory determined that the critical mass ofneptunium-237 is about 60 . The critical mass of a fissionable material is the minimum amount that must be brought

together to start a chain reaction. This element has a density of 19.5 .

Part A

What would be the radius of a sphere of this material that has a critical mass?

Express your answer using two significant figures.

ANSWER:

Correct

Exercise 1.16

Part A

How many gallons of gasoline are used in the United States in one day? Assume two cars for every three people,

l + tm2/3 l2t−2

[a]

l m t

a

a = Δv/Δt Δ

= [a] l

t2

kgg/cm3

= 9.0 r cm

mi



that each car is driven an average of 10,000 per year, and that the average car gets 20 miles per gallon.

ANSWER:

Correct

Adding and Subtracting Vectors Conceptual Question

Six vectors (A to F) have the magnitudes and directions indicated in the figure.

Part A

Which two vectors, when added, will have the largest (positive) x component?

Hint 1. Largest x component

The two vectors with the largest x components will, when combined, give the resultant with the largest xcomponent. Keep in mind that positive x components are larger than negative x components.

ANSWER:

mi

gal/day

gal/day

gal/day

gal/day

8.9 × 107

4.5 × 109

1.1 × 108

2.8 × 108



Correct

Part B

Which two vectors, when added, will have the largest (positive) y component?

Hint 1. Largest y component

The two vectors with the largest y components will, when combined, give the resultant with the largest ycomponent. Keep in mind that positive y components are larger than negative y components.

ANSWER:

Correct

Part C

Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largestmagnitude?

Hint 1. Subtracting vectors

To subtract two vectors, add a vector with the same magnitude but opposite direction of one of the vectors tothe other vector.

ANSWER:

C and E

E and F

A and F

C and D

B and D

C and D

A and F

E and F

A and B

E and D



Correct

Resolving Vector Components with Trigonometry

Often a vector is specified by a magnitude and a direction; for

example, a rope with tension exerts a force of magnitude in a direction 35 degrees north of east. This is a good way

to think of vectors; however, to calculate results with vectors,it is best to select a coordinate system and manipulate thecomponents of the vectors in that coordinate system.

Part A

Find the components of the vector with length and angle with respect to the x axis as shown, named . Don't

forget that when multiplying two factors, you must include a multiplication symbol; also, the cos and sin functionsmust have parentheses around their arguments. For example, a vector might take the form p*sin(Q),m*cos(N).

Write the components in the form x,y.

Hint 1. What is the x component?

The x component is .

ANSWER:

A and F

A and E

D and B

C and D

E and F

T T

a α A

acos(α)

= A acos(α),asin(α)



Correct

Part B

Find the components of the vector with length and angle with respect to the x axis as shown, named .

Write the components in the form x,y.

ANSWER:

Correct

Notice that vectors and have the same form despite their placement with respect to the y axis on the

drawing.

Part C

Find the components of the vector with length and angle as shown, named .

Express your answer in terms of and . Write the components in the form x,y.

Hint 1. Consider the vector's direction

Be careful of the sign of the components.

Hint 2. What is angle relative to?

Angle differs from the other two angles because it is the angle between the vector and the y axis, unlike

the others, which are with respect to the x axis.

ANSWER:

Correct

Exercise 1.32

Vector is in the direction 31.0 clockwise from the - -axis. The -component of is = -16.0 .

b β B

= B bcos(β),bsin(β)

A B

c ϕ C

c ϕ

ϕ

ϕ

= C −csin(ϕ),ccos(ϕ)

A ∘ y x A Ax m



Part A

What is the -component of ?

Express your answer with the appropriate units.

ANSWER:

Correct

Part B

What is the magnitude of ?

Express your answer with the appropriate units.

ANSWER:

Correct

Exercise 1.34

A postal employee drives a delivery truck over the route shown in the figure .

Part A

Use the method of components to determine the magnitude of her resultant displacement.

y A

= -26.6 Ay m

A

= 31.1 A m




ANSWER:

Correct

Part B

Use the method of components to determine the direction of her resultant displacement.


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 walk1.25 at 30.0 west of north, and finally walk 1.00 at 40.0 north of east, where you find the treasure: abiography of Isaac Newton!

Part A

To return to the old oak tree, in what direction should you head ? Use components to solve this problem.

ANSWER:

Correct

Part B

To return to the old oak tree, how far will you walk? Use components to solve this problem.

ANSWER:

Correct

7.8 km

38 North of East ∘

mkm ∘ km ∘

= 8.90 west of south θ ∘

= 911 D m



Exercise 1.44

Part A

Is the vector a unit vector?

ANSWER:

Correct

Part B

Justify your answer.

ANSWER:

Submitted, grade pending

Part C

Can a unit vector have any components with magnitude greater than unity?

ANSWER:

Correct

Part D


ANSWER:

( + + )i j k

Yes.

No.

3693 Character(s) remaining

i,j, and k are all equal to 1. The magnitude of a unit vector must be equal to one. This one equals sqrt(3)

Yes.

No.




Part E

Can it have any negative components?

ANSWER:

Correct

Part F


ANSWER:


Part G

If 2.0 8.0 , where is a constant, determine the value of that makes a unit vector.

Express your answer numerically using two significant figures. If there is more than one answer, entereach answer separated by a comma.

ANSWER:


Again, the unity has to equal 1. Squaring something greater than 1 and adding it to something else will cause the magnitude to be greater than one.

Yes.

No.


Components are squared so negative components are ultimately positive.

= a(A +i )j a a A

= 0.121,-0.121a



All attempts used; correct answer displayed

Exercise 1.46

Part A

Given two vectors 4.20 7.80 and 5.80 2.40 , find the scalar product of the two vectors

and .

ANSWER:

Correct

Part B

Find the angle between these two vectors.

ANSWER:

Correct

Exercise 1.50

Part A

For the two vectors in the figure , find the magnitude of the vector product .

=A +i j =B −i j A

B

= 5.64⋅A B

= 84.2 θ ∘

×A B



ANSWER:

Correct

Part B

Find the direction of the vector product .

ANSWER:

Correct

Part C

Find the magnitude of .

ANSWER:

Correct

Part D

4.61 cm2

×A B

+z-direction

-z-direction

×B A

4.61 cm2

×



Find the direction of .

ANSWER:

Correct

Exercise 1.48

Part A

Given two vectors and , find the vector product (expressed in

unit vectors).

Express your answer in terms of the unit vectors , , and .

ANSWER:

Correct

Part B

What is the magnitude of the vector product?

ANSWER:

Correct

Score Summary:

Your score on this assignment is 94.7%.You received 12.31 out of a possible total of 13 points.

×B A

+z-direction

-z-direction

= 4.00 + 7.00A i j = 5.00 − 2.00B i j ×A B

i j k

= ×A B −43k

= 43.0| × |A B

Date post:	18-Jan-2016
Category:	Documents
Upload:	fatboy91
View:	857 times
Download:	0 times

Chapter 01 Homework

Documents