Biomedical Engineering Reference
In-Depth Information
(2 kg)(10 m/s
2
)
d
⊥
; the negative sign indicates that the
rotation is clockwise around the shoulder.
(a)
M
W
¼
mgd
⊥
¼
(0.70 m)sin 30
¼
As
d
⊥
¼
(0.70 m)0.5
¼
0.35 m,
(2 kg)(10 m/s
2
)(0.35 m)
M
W
¼
¼
7Nm.
(2 kg)(10 m/s
2
)(0.7 m)
(b)
M
W
¼
¼
14 N m.
To maintain the arm outstretched horizontally (
θ ¼
90
) in equilibrium, pre-
venting its fall, it is necessary to apply a muscle force to counteract the torque. This
force will be twice as large as the force to maintain the arm at 30
.
Let us see now what happens when the same object is hanging at the elbow with
the arm outstretched horizontally. In this case, the torque will decrease to almost
half of that with the weight on the hand, because the lever arm has been decreased to
almost half. This means also that the muscle has to exert a force around half of the
previous example to maintain it outstretched.
Exercise 2.1
Consider that a package of sugar of 1 kg is in the hand of a horizon-
tally outstretched arm. Find the torque due to the weight of the sugar package about
the axis of rotation passing through the:
(a) Wrist
(b) Elbow
(c) Shoulder
Consider the following distances: shoulder-elbow
¼
25 cm, elbow-wrist
6 cm.
(d) Repeat the exercise, considering that the arm is held upward at a 30
angle to
the body and then downward at the same angle.
Exercise 2.2
Discuss the reason for progressive difficulty in abdominal exercises,
lying flat on the back: (a) with outstretched arms and the hands in the direction of
the feet, (b) with the arms crossed over the chest, and (c) with the fingers interlaced
under the head.
¼
22 cm, and wrist-center of the hand
¼
Exercise 2.3
Consider a person in the yoga posture called sarvanga-asana, as
shown in the figure of Exercise 2.3. At the beginning, the person is lying flat
on his back, with his legs outstretched. Then, slowly, the legs are lifted until
the toes are pointed straight up. To reach the final posture, it is recommended that
persons with problems in their spinal column bend their legs before lifting them.
Discuss why.
