Problem 3.1 As illustrated in Fig. 3.13, consider a diver of 88 kg mass standing

Question

Problem 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 hoard, 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 = 3.979 N-m. Answer l- 3.5 m. Problem 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 = 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. Determine the moment generated about point O by the weights of the divers and the board. Calculate the net moment about point O. Answer M1 = 3. 371.2 N-m; M2 = 1,607.2 N-m: Mb = 2,548 N-m; Mnet = 7,526.4 N-m. Problem 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.

Explanation / Answer

Problem 3.2 ::

Moment generated by diver at B is given as

Mb = weight x OB = mgl = 86 x 9.8 x 4 = 3371.2 N

Moment generated by diver at A is given as

Mb = weight of second diver x OA = mgl/2 = 82 x 9.8 x 2 = 1607.2 N

Moment generated by diver at A is given as

Mb = weight of board x OA = mgl/2 = 170 x 9.8 x 2 = 3332 N

net moment = 3371.2 + 1607.2 + 3332 = 8310.4

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