Example 5 The drop gate at the end of the trailer has a mass of 1.25 Mg and mass center at G. If it is supported by the cable AB and hinge at C, determine the maximum deceleration of the truck so that the gate does not begin to rotate forward. What are the horizontal and vertical components of reaction at the hinge C? B 30° 1.5 m 1 m

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The position of the head and neck and the forces acting on the head are shown in the figure. The center of gravity of the head of mass m=9 kg is located at point C. The joint reaction force of F J = 150 N, which makes an angle of α = 30° with the vertical from the point B, is acting on the skull by the neck extensor muscles. The center of the atlantooccipital joint is located at point B. For this flexion position of the head, the neck muscle force FM, which makes an angle of γ with the horizontal from the point A , is effective . (Take the gravitational acceleration g as 9.81 m/s 2. ) Accordingly; a)   Calculate the angle γ of the muscle force F M with the horizontal. b)   Calculate the muscle strength F M. (Write your result in N units.)

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