Fundamental of biomechanics

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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