Question

Question 2. 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 Fig. 2(a) is analysed. The hip joint Ois assumed to remain fixed relative to the car, and the torso above the hip is treated as a nonuniform rigid body of mass m pivoted at 0. The centre of mass of the torso is at G, which is at a distance from with the initial position of og taken as vertical (i.c. 8 = 0). The radius of gyration of the torso about ois ko. The acceleration due to gravity is denoted by g. The car is brought to a sudden stop in a crash test with a constant deceleration ac- 0). Obtain a general expression for the angular acceleration of the torso in [10 marks) terms of r, ko.. , and a after the crash (.e. after the application of deceleration 2) considering the general position shown in Fig. 2(a) (i.e. the torso shown by dashed line). (ii) Using MATLAB'S ODE solvers, solve the equation obtained for the [12 marks] angular acceleration in () and obtain the angular velocity of the torso when 8 = 45°. Use: m = 40 kg.r = 40 cm, k, = 50 cm, and a = 10g, where g is the acceleration due to gravity, assume the torso is in the vertical position before the impact (iii). Assuming at 8 = 45° the torso's hcad hit the panel (i.e. Bpanel = 45°; [3 marks] see Fig. 2(b)), determine the impact vclocity assuming l = 75 cm. (iv). Write a MATLAB script or function which, for given values of ac and [20 marks] panel, calculates: (1) The head impact velocity (2) The time it takes for the model's head to hit the panel. Then plot both quanities versus ac for ac in the range [1g 10g) assuming paner"(30+ a), and discuss the results. Important note: a in panel is the sum of the last digit of group members' student numbers. For instance, for last digits of 5 and 6, x is 11 and panel - (30 +11° = 41'. The question is continued on the next page. Fig. 2(a) Fig. 2(b) Page of 5
a=11

Answer 1

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