Questions 3.1, 3.2, 3.3, 3.4, 3.5
3.1 As illustrated in Fig. 3.13, consider a diver of
88 kg mass standing on the free end of a horizontal diving
board at point B, preparing for a jump. The diving board has
a uniform thickness and a mass of 56 kg, and it is mounted to
the ground at point O. Point A indicates the center of gravity
of the diving board, and it is equidistant from points O and B.
Determine the length of the diving board (l) if the net
moment generated about point O by the weight of the diver
and the diving board is MO ¼ 3; 979 N-m.
3.2 As illustrated in Fig. 3.30, consider two divers
preparing to dive into a pool in a sequence. The horizontal
diving board of uniform thickness is mounted to the ground at
point O, has a mass of 170 kg, and l ¼ 4 m in length. The first
diver has a mass of 86 kg and he stands at point B, which is the
free end of the diving board. The second diver has a mass of
82 kg and he stands at point A, which is the center of gravity of
the board. Furthermore, point A is equidistant from points O
and B.
3.3 Consider a person using an exercise apparatus
who is holding a handle that is attached to a cable (Fig. 3.31).
The cable is wrapped around a pulley and attached to a
weight pan. The weight in the weight pan stretches the
cable and produces a tensile force F in the cable. This
force is transmitted to the person’s hand through the handle.
3.4 Figure 3.32 illustrates a simplified version of a
hamstring strength training system for rehabilitation and
athlete training protocols. From a seated position, a patient
or athlete flexes the lower leg against a set resistance provided
through a cylindrical pad that is attached to a load. For
the position illustrated, the lower leg makes an angle y with
the horizontal. Point O represents the knee joint, point A is
the center of gravity of the lower leg, W is the total weight of
the lower leg, F is the magnitude of the force applied by the
pad on the lower leg in a direction perpendicular to the
3.5 As illustrated in Fig. 3.33, consider an athlete
performing flexion/extension exercises of the lower arm to
strengthen the biceps muscles. The athlete is holding the
weight of W1 ¼ 150 N in his hand, and the weight of his
lower arm is W2 ¼ 20 N. As measured from the elbow
joint at point O, the center of gravity of the lower arm (point
A) is located at a distance a ¼ 7:5 cm and the center of
gravity of the weight held in the hand is located at a distance
b ¼ 32 cm.
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