 1 
30
o
A
= 20
3
N
60
o
B
= 20
N
45
o
A
= 30
2
m
30
o
B
= 10
3
m
C
= 10 m
1.
For each vector system drawn, write all the vectors in Cartesian (XY) notation.
(i)
(ii)
2.
For each of the vector systems above, write the resultant vector in both Cartesian (XY) format and polar form.
3.
For each of the following equations, solve for all the variables:
(i)
2
3
2
5
−
=
+
x
x
(ii)
3
4
5
=
+
y
x
and
y
x
5
11
=
+
(iii)
1
=
+
+
z
y
x
and
4
3
5
2
=
−
−
z
y
x
and
2
3
−
=
+
z
y
4.
Five lightweight plastic spheres labeled A through E are suspended from threads as shown.
Each sphere
holds either positive charge +Q, negative charge –Q, or
zero charge.
When each sphere is moved closed to
another, the following behavior is noticed:
Sphere A attracts ALL the other spheres.
Sphere B attracts spheres A, C, and D only, and has no effect on sphere E.
A positive charge repels sphere C.
A
B
C
D
E
N
y
3
10
x
10

)
y
sin60
x
(cos60
N
20
N
y
3
10
x
30
)
y
sin30
x
(cos30
N
3
20
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
+
=
+
=
+
=
+
=
B
A
r
r
m
y
10
C
m
y
3
5
x
15

)
y
sin30
x
(cos30
m
3
10
m
y
30
x
30
)
y
sin45
x
(cos45
m
2
30
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
=
+
=
+
=
+
=
+
=
r
r
r
B
A
For (i)
N
y
3
20
x
20
ˆ
ˆ
+
+
=
+
B
A
r
r
magnitude =
N
40
3
20
20
2
2
=
+
)
(
)
(
angle =
o
1

60
20
3
20
tan
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
θ
For (ii)
m
y
)
3
5
20
(
x
15
ˆ
ˆ
+
+
+
=
+
+
C
B
A
r
r
magnitude =
m
3
32
3
5
20
15
2
2
.
)
(
)
(
=
+
+
angle =
o
1

4
62
15
3
5
20
tan
.
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
=
θ
Crossmultiply
3(x+2) = 5(x2)
3x + 6 = 5x – 10;
2x = 16;
x = 8
Substitute
x = 5y11
5(5y11) + 4y = 3;
25y – 55 + 4y = 3;
29y = 58;
y=2 so then x = 1
Substitute x = 1yz into eqn 2 to get 2(1yz) 5y 3z = 4 or
2 7y 5z = 4
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 Spring '08
 Giese
 Charge, Work, Electric charge

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