The car bumper is made of polycarbonate polybutylene terephthalate. If \(E=2.0 \mathrm{GPa}\), determine the maximum deflection and maximum stress in the bumper if it strikes the rigid post when the car is coasting at \(v=0.75 \mathrm{~m} / \mathrm{s}\). The car has a mass of \(1.80 \mathrm{Mg}\), and the bumper can be considered simply supported on two spring supports connected to the rigid frame of the car. For the bumper take \(I=300\left(10^{6}\right) \mathrm{mm}^{4}\), \(c=75 \mathrm{~mm}, \sigma_{Y}=30 \mathrm{MPa}\) and \(k=1.5 \mathrm{MN} / \mathrm{m}\).

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k 0.9 m 0.9 m v=0.75 m/s