Problem 4.1 As illustrated in Figure 4.49, consider an 80 kg person preparing to dive into a pool. The diving board is rep-resented by a uniform, horizontal beam that is hinged to the ground at A and supported by a frictionless roller at D. B is a point on the board directly under the center of gravity of the person. The distance between A and B is = 6 m and the distance between A and D is d = 2 m. (Note that one-third of the board is located on the left of the roller support and two-third sis on the right. Therefore, for the sake of force analyses, one can assume that the board consists of two boards with two different weights connected at D.) If the diving board has a total weight of 1500 N, determine the reactions on the beam at A and D.
Problem 4.2 The uniform, horizontal beam shown in Figure 4.50is hinged to the ground at A and supported by a frictionless roller at D. The distance between A and B is = 4 m and the distance between A and D is d = 3 m. A force that makes an angle B = 60° with the horizontal is applied at B. The magnitude of the applied force is P 1000 N. The total weight of the beam isW = 400 N.= By noting that three-quarters of the beam is on the left of the roller support and one-quarter is on the right, calculate the x and y components of reaction forces on the beam at A and D.
6. A person is performing a set of squats. The time for the upward movement and the downward movement is the same, assume that when squatting down no work is performed. h1= 0.5m (initial height of total center of mass) h2=1.6 m (final height of total center of mass) t=1.2 s (time to go from h1 to h2) n=8 (number of repetitions) trợr-19.2s (total time) m=62kg (mass of the person) m2=50kg (mass of the barbell) mechanical work performed per repetition total mechanical work average power per repetition total average power total average power per kg of body mass
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