Problem Set # 8
Giancoli 4
th
ed.
12.16. (
a
)
Calculate the torques about the elbow joint (the dot in the
free
body diagram). The arm is in equilibrium. Take counterclockwise
torques as positive.
(
)
(
)
(
)
(
)
(
)
M
2
M
o
sin
0
3.3 kg
9.80m s
0.24 m
249.9N
sin
0.12 m sin15
250N
F
d
mgD
mgD
F
d
!
"
=
#
=
$
=
=
=
%
(
b
) To find the components of
J
,
F
write Newton’s second law for both the
x
and
y
directions. Then
combine them to find the magnitude.
(
)
(
)
(
)
(
)
(
)
(
)
J
M
J
M
M
J
2
J
M
2
2
2
2
J
J
J
cos
0
cos
249.9N cos15
241.4N
sin
0
sin
249.9N sin15
3.3kg
9.80m s
32.3N
F
241.4N
32.3N
243.6N
240N
x
x
x
y
y
y
x
y
F
F
F
F
F
F
F
mg
F
F
F
mg
F
F
=
"
=
#
=
=
=
=
"
"
=
#
=
"
=
°
"
=
=
+
=
+
=
$
°
%
%
12.19. There will be a normal force upwards at the ball of the foot,
equal to the person’s weight
(
)
N
.
F
mg
=
Calculate torques about
a point on the floor directly below the leg bone (and so in line with
the leg bone force,
B
F
!
). Since the foot is in equilibrium, the sum
of the torques will be zero. Take counterclockwise torques as
positive.
(
)
(
)
(
)
N
A
2
A
N
2
0
2
2
2 72 kg
9.80m s
1400N
F
d
F d
F
F
mg
=
"
=
#
=
=
=
=
$
The net force in the
y
direction must be zero. Use that to find
B
.
F
N
A
B
B
N
A
0
2
3
2100N
y
F
F
F
F
F
F
F
mg
mg
mg
=
+
!
=
"
=
+
=
+
=
=
#
12.21. (
a
)
The pole is in equilibrium, and so the net torque on it
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 Fall '07
 Mueller
 Physics, Buoyancy, Force, Archimedes, Fundamental physics concepts, net torque

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