Selected Problems from Chapter 3. 45 o.
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Transcript of Selected Problems from Chapter 3. 45 o.
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Selected Problems from
Chapter 3
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. (2 4 ).(4 2 ) 8 8 0
.cos 0 90o
A B i j i j
A B
AB
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B,C
2 2 2B,C
B,C
B,C
Let's call the dissplacements A, B and C respectively.
The resultant R = B + C
where R = 2.5 2.5 2 2.5 2.5 2 3.5
R makes an angle x =45 with B so it is along A
the resultant R = A + R
B C m
A B
2.5 3.5 6.0 in the direction of A
C
R m
B,CR
AB
C
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1 13 3
1 13 3
2 2 21 13 3
rearange to get
= ( 2 ) (15 21 ) 2(3 6 )
15 21 6 12 ) (15 6 9 )
15 ( 6) 9 225 36 81 6.16
C B A i k j k
i k j k i j k
C
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you could start from point O and return to it counterclockwise:
( ) ( ) 0
put on the left-hand side and rest on the right-hand side:
you get
R A B C D
C
C D B A
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O
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.( ) 0
:
. 0
k k i
because
k i j
k j
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. ( 2 ).(2 3 ) 2 6
. 4
2 6 4 10 / 2 5
A B ai j i j a
A B
a a
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����������������������������
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45o
A��������������
B��������������
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30o R
A
B
C
A = -4.65 i
B = -(12.7 sin 30o)i + (12.7 cos 30o)j = -6.35 i + 11.0 jC = 11.0 i
R = A+B+C= -4.65 i + (- 6.35 i + 11.0 j) + 11.0 i
- = 11.0 i +11.0i + 11.0j = 11.0 j (11.0 km due north)
take i (east) j(north) -i (west) -j (south)
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30o
A
A = (3.0 cos 30o) i + (3.0 sin 30o) j = 2.6 i + 1.5 j
B = - 2 A = -2 (2.6 i + 1.5 j) = - 5.2 i - 3.0 j
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** What angle does a = -5i + 3 j – 2 k make with the z- axis
109)324.0cos(
,324.016.6
00.2cos
16.64925
,1
00.2).(.
,cos.
a
k
k 2.00- j 3.00 i5.00-kak
akak