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Chapter 3 Homework
Due: 9:00am on Monday, September 14, 2009
Note: To understand how points are awarded, read your instructor's Grading Policy.
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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 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 the components of the
vectors in that coordinate system.
Part A
Find the components of the vector
Hint A.1
with length
= 1.00 and angle
=20.0 with respect to the x axis as shown.
What is the x component?
Look at the figure shown.
points in the positive x direction, so
is positive. Also, the magnitude
is just the length
.
Enter the x component followed by the y component, separated by a comma.
ANSWER:
= 0.940,0.342
Correct
Part B
Find the components of the vector
Hint B.1
with length
= 1.00 and angle
=15.0 with respect to the x axis as shown.
What is the x component?
Hint not displayed
Enter the x component followed by the y component, separated by a comma.
ANSWER:
The components of
= 0.966,0.259
Correct
still have the same form, that is,
, despite
's placement with respect to the y axis on the drawing.
Part C
Find the components of the vector
Hint C.1
with length
= 1.00 and angle
Method 1: Find the angle that
25.0 as shown.
makes with the positive x axis
Hint not displayed
Hint C.2
Method 2: Use vector addition
Hint not displayed
Enter the x component followed by the y component, separated by a comma.
ANSWER:
= -0.423,0.906
Correct
Problem 3.36
A cannon tilted upward at 35.0 fires a cannonball with a speed of 90.0
.
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Part A
What is the component of the cannonball's velocity parallel to the ground?
ANSWER:
= 73.7
m/s
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 x component?
Hint A.1
Largest x component
Hint not displayed
ANSWER:
C and E
E and F
A and F
C and D
B and D
Correct
Part B
Which two vectors, when added, will have the largest y component?
Hint B.1
Largest y component
Hint not displayed
ANSWER:
C and D
A and F
E and F
A and B
E and D
Correct
Part C
Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude?
Hint C.1
Subtracting vectors
Hint not displayed
ANSWER:
A and F
A and E
D and B
C and D
E and F
Correct
Problem 3.25
For the three vectors shown above in the figure,
1.90 . What is vector
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Part A
Write
as components separated by a comma. For example, if you thought the x component was 3 and the y component was 4, then you would enter 3,4.
ANSWER:
= -5.90,2.00
Correct
Part B
What is the magnitude of
ANSWER:
?
= 6.23
Correct
Part C
How many degrees above the negative x-axis does
ANSWER:
point?
= 18.7
Correct
-
Problem 3.45
Three forces are exerted on an object placed on a tilted floor in the figure. The forces are measured in newtons ( ).
Part A
Assuming that forces are vectors, what is the component of the net force
ANSWER:
parallel to the floor?
= -0.500
Correct
Part B
What is the component of
perpendicular to the floor?
ANSWER:
= 1.67
N
Correct
Part C
What is the magnitude of
?
ANSWER:
= 1.74
Correct
Part D
What is the direction of
ANSWER:
?
= 73.3
Correct
above the floor on the left side of
Vector Addition in a Unit Cell
In nature, substances often possess a crystalline structure. The basic component of a crystal is the unit cell, such as the rectangular parallelpiped illustrated in the figure . (For the purposes of this problem, take
and
,
,
to be positive.)
Find the following quantities. When the question asks for a vector, express your answer as an ordered triplet. That is, a vector with length
length in the y direction, and length in the z direction should be written as
.
in the x direction,
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Part A
What is the vector
from point O to point E?
ANSWER:
=
Correct
Part B
What is the vector
from point O to point F?
ANSWER:
=
Correct
Part C
What is the vector
from point O to point C?
ANSWER:
=
Correct
Part D
Hint D.1
How to use the components
Hint not displayed
ANSWER:
=
Correct
Part E
Hint E.1
The meaning of |
|
Hint not displayed
Hint E.2
Length of a vector
Hint not displayed
ANSWER:
|
|=
Correct
Part F
Hint F.1
Consider geometry
Use Pythagorean triangles to calculate the length of the vector.
ANSWER:
|
|=
Correct
Part G
ANSWER:
|
|=
Correct
Score Summary:
Your score on this assignment is 98.7%.
You received 54.29 out of a possible total of 55 points.
9/13/2009 9:46 PM