Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_85

6/85 In a study of head injury against the instrument panel of a car during sudden or crash stops where lap belts without shoulder straps or airbags are used, the segmented human model shown in the figure is analyzed. The hip joint \(O\) is assumed to remain fixed relative to the car, and the torso above the hip is treated as a rigid body of mass \(m\) freely pivoted at \(O\). The center of mass of the torso is at \(G\) with the initial position of \(OG\) taken as vertical. The radius of gyration of the torso about \(O\) is \(k_O\). If the car is brought to a sudden stop with a constant deceleration \(a\), determine the speed \(v\) relative to the car with which the model's head strikes the instrument panel. Substitute the values \(m = 50\text{ kg}\), \(\bar{r} = 450\text{ mm}\), \(r = 800\text{ mm}\), \(k_O = 550\text{ mm}\), \(\theta = 45^\circ\), and \(a = 10g\) and compute \(v\).