Version A
1.
Units and Vectors (8 points)
a.
In SI units, energies are measured in units called Joules, where
1.00 Joule = 1.00 kg m
2
/s
2
.
An alternative unit of energy is the Dyne:
1.00 Dyne = 1.00 g cm
2
/s
2
.
How many Dynes are there in 2.50 Joules?
2
3
2
2
2
7
2
2
10 g
10 cm
1Dyne
2.50 kg m /s
2.50
10 Dynes
kg
m
1.00 g cm /s
⎛
⎞
⎛
⎞
⎛
⎞
×
×
×
=
×
⎜
⎟
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
⎝
⎠
A: 2.50×10
7
Dynes
B: 4.25×10
7
Dynes
C: 6.50×10
7
Dynes
D: 6.50×10
7
Dynes
b.
The vector
A
has a magnitude of 5.00 m, and is oriented at an angle of +30.0°
from the x axis.
Find a vector
B
(in the form B
x
i
+ B
y
j
) so that
A
–
B
has a
magnitude of 4.00 m and is oriented in the direction of the positive y axis.
(
)
(
)
(
)
(
)
(
)
(
)
(
)
4.00 m
5.00 m cos
5.00 m sin
0
5.00 m cos
4.33 m
4.00 m
5.00 m sin
4.00 m
1.50 m
4.33 m
1.50 m
y
x
y
x
x
x
x
x
y
y
y
y
y
y
A
B
C
j
C
j
A
A
C
A
B
B
A
C
A
B
B
A
C
B
i
j
θ
θ
θ
θ
−
=
= +
=
=
=
=
=
−
=
=
= +
=
=
−
=
−
=
−
= −
= +
+ −
G
G
G
G
G
G
G
G
A: B
x
= 4.33 m, B
y
= -1.50 m
B: B
x
= 4.60 m, B
y
= +0.857 m
C: B
x
= 6.58 m, B
y
=
+0.394 m
D: B
x
= 0.867 m, B
y
= -2.50 m

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