18 solution q. E. D

Work. Referring to the FBD of the reel, Fig. a, only force P does positive work. When 
the reel rotates 2 revolution, force P displaces S
=
u
r
=
2(2
p
)(0.75)
=
3
p
m. Thus
U
p
=
P
s
=
60(3
p
)
=
180
p
J
Principle of Work and Energy.
T
1
+
Σ
U
1
-
2
=
T
2
0
+
180
p
=
36.0 
v
2
v
=
3.9633 rad
>
s
=
3.96 rad
>
s 
Ans.
0.75 m
0.6 m
1 m
P
A
O
B
Ans:
v
=
3.96 rad
>
s

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916
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18–5.
A force of 
P
=
20 N is applied to the cable, which causes 
the 175-kg reel to turn since it is resting on the two rollers 
A
and 
B
of the dispenser. Determine the angular velocity of 
the reel after it has made two revolutions starting from rest. 
Neglect the mass of the rollers and the mass of the cable. 
The radius of gyration of the reel about its center axis is 
k
G
=
0.42 m.
SOLUTION
T
1
+
Σ
U
1
-
2
=
T
2
0
+
20(2)(2
p
)(0.250)
=
1
2
3
175(0.42)
2
4
v
2
v
=
2.02 rad
>
s