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 0 is 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 r from 0, with the initial position of OG taken as vertical (i.e. 0 = 0). The radius of gyration of the torso about 0 is 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.

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Answer 1

clc;clear all;close all;
T=0:0.0001:1;%time 0 to 1sec
g=9.81;%value acceleration due to gravity
fun=@(t,x)[x(2);16*g*cos(x(1))+1.6*g*sin(x(1))];%state space function
IC=[0;0];%initial condition
[t,y] = ode45(fun,T,IC);
y(:,1)=y(:,1)*180/pi;%to convert rad to degree
i=1;
while y(i,1)<45
i=i+1;
end
fprintf('The angular velocity at theta=%1.0fdegree is:%1.3frad/sec\n',y(i-1,1),y(i-1,2))

>ma r img lod OX fuse body diagram At Dynamic equilibrium, Imoro max rcos9 + ting xy sino - Iod. 40x10x9 x 0.4COSE + hogx0.4 sino - 4ox0.52 ö by to oesoo - Quis640 + 8 son 67 691- Quis69.1t geen o'. form! state space X=0 0 36,- *2 = = 16gcoso tlebgsino x2 = 1690sx, + libgsins, Initial condition. cod=0 [x,10) = logost, tlibgsins, x = x2 810)=0 (alle X

Matlab Result:

The angular velocity at theta=45degree is:15.212rad/sec
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