Biomedical Engineering Reference
In-Depth Information
(a) M W ¼
4.5 N m.
(b) If the forearm is in rotational equilibrium, the magnitude of the torque due to
the muscle force must be equal to that calculated in (a) with the opposite sign,
that is, M b ¼
(15 N)(0.30 m)
¼
4.5 N m
¼
F b (0.035 m).
Hence, F b ¼
¼
128.6 N. Note that the muscle force is 8.6
times larger than the weight of the object.
Exercise 2.7 In Example 2.4, the weight of the forearm and hand was neglected.
Consider now that the weight of the forearm plus the hand of 20 N is applied at
15 cm from O. Find:
(4.5 N m)/(0.035 m)
(a) The torque due to the weight of the forearm-hand
(b) The muscle force exerted by the biceps muscle
2.6 Answers to Exercises
Exercise 2.1 (a) M
5.30 N m; the same
result is obtained when the angle between the outstretched arm and the body is 30 ,
either upward or downward since d is always equal to d sin30 : (d) M
¼
0.60 N m; (b) M
¼
2.80 N m; (c) M
¼
¼
0.30 N m;
(e) M
2.65 N m. The direction of rotation depends on the arm,
either the left or the right arm.
¼
1.40 N m; (f) M
¼
Exercise 2.2 The progressive difficulty is due to the increase in the magnitude of
torque which is a consequence of the increase in the distance of application of total
weight (head-neck + torso + arms-forearms-hands and a part of the abdomen) to
the axis of rotation at the lower abdominal region. As the arms-forearms-hands are
brought closer to the head, the torque becomes larger. To overcome it, a larger
torque with the opposite direction of rotation should be exerted, which demands
larger muscle force.
Exercise 2.3 As the angle of the set thigh-leg-foot with the ground (horizontal)
becomes smaller, the torque becomes larger, because the distance d is larger, and
the weight of the set is applied a little above the knee. As the leg is elevated, the
torque will be less because the distance d will be less. If the torque is larger, this
must be equilibrated by another torque of opposite sign produced by muscle force.
Therefore, the larger the torque, the larger the muscle force should be in order to
maintain equilibrium. Bending the legs, the torque due to the weight will be much
less, because the distance d will shorten and the muscle needs to exert a much
smaller force to reach the final posture of sarvanga-asana.
Exercise 2.4 M
¼
20 N m.
Exercise 2.5 m A ¼
10 g; m B ¼
50 g; m C ¼
26.7 g.
Exercise 2.6 (a) M
3.0 N m; (b) the torque of the force exerted by the biceps
muscle must equilibrate the sum of torques due to the weight of the object plus the
weight of the forearm-hand. So, F b ¼
¼
214.3 N.
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