 1 
Physics 112  HW #12 Solutions
Fall 2005
1178
[Dragging A Hay Bale]
(a) Since the bale is moving at constant velocity, the net force on
it is zero.
∑
F
x
= F – f
k
= 0
⇒
F = f
k
(1)
∑
F
y
= N – w = 0
⇒
N = mg
(2)
Since block is sliding, f
k
=
µ
k
N =
µ
k
mg
Substituting for f
k
into eq. (1), we have
F =
µ
k
mg
= (0.35)(30.0 kg)(9.81 m/s
2
) =
103 N
(b) When block is about to tip about edge A (see diagram), the
normal force N is acting at that edge, and the net torque about A
is zero.
∑
τ
A
=
w(0.125 m) – F h = 0
⇒
h
=
w(0.125 m)
F
=
(30.0 kg)(9.81 m/s
2
)(0.125 m)
103 N
=
0.357 m
1039
[Block on String]
(a) Yes, angular momentum of the block is conserved, because there are no forces that can exert a
torque on the block.
(b) L
f
=
L
i
so m R
f
2
ω
f
=
m R
i
2
ω
i
ω
f
=
R
i
2
R
f
2
ω
i
=
(0.300 m)
2
(0.150 m)
2
1.75 rad/s
=
7.00 rad/s
(c) Change in KE of block is
K
f
 K
i
=
½ mR
f
2
ω
f
2
 ½ mR
i
2
ω
i
2
= ½ (0.0250 kg)[ (0.150 m)
2
(7.00 rad/s)
2
 (0.300 m)
2
(1.75 rad/s)
2
] =
1.03 x 10
2
J
(d) The work done in pulling on the cord is equal to the change in KE of the block, so
W =
1.03 x 10
2
J
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 2 
1040
[Spinning Figure Skater]
Angular momentum is conserved, so L
f
=
L
i
I
f
ω
f
=
I
i
ω
i
[ I
body
+ I
arms wrapped
]
ω
f
=
[I
body
+ I
arms out
]
ω
i
ω
f
=
[ 0.40 kg m
2
+
(
1
/
12
) (8.0 kg)(1.8 m)
2
]
[ 0.40 kg m
2
+ (8.0 kg)(0.25 m)
2
]
(0.40 rev/s)
=
1.14 rev/s or 7.15 rad/s
1043
[Parachuting onto a Turntable]
(a)
Vertical landing
⇒
Cons. of Angular Momentum about turntable axis:
L
before
=
L
after
⇒
I
i
ω
i
=
I
f
ω
f
I
i
=
1
2
MR
2
=
1
2
(120 kg)(2.00 m)
2
=
240 kgm
2
I
f
=
1
2
MR
2
+ mR
2
=
240 kgm
2
+ (70 kg)(2.00 m)
2
=
520 kgm
2
∴
ω
f
=
I
i
I
f
ω
i
=
240 kgm
2
520 kgm
2
(3.00 rad/s)
=
1.38 rad/s
(b) K
i
=
1
2
I
i
ω
i
2
=
1
2
(240 kgm
2
)(3.00 rad/s)
2
=
1080 J
K
f
=
1
2
I
f
ω
f
2
=
1
2
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '07
 LECLAIR,A
 mechanics, Angular Momentum, Force, Kinetic Energy, kg, VE

Click to edit the document details