Automobiles must be designed to survive a frontal impact. Specifically, the design must allow low speed impacts with little damage, while allowing the vehicle front end structure to deform and absorb impact energy at higher speeds. Consider a frontal impact test of a vehicle with a mass of 1000 kg. a. For a low speed test at 2.5 m/s, compute the energy in the vehicle just prior to impact. If the bumper is a pure elastic element; what is the effective design stiffness required to limit the bumper maximum deflection during impact to 4 cm?
b. At a higher speed impact of 25 m/s, considerable deformation occurs. To absorb the energy the front end of a vehicle is designed to deform while providing a nearly constant force. For this condition, what is the amount of energy that must be absorbed by the deformation [neglecting the energy stored in the elastic deformation in (a)]? If it is desired to limit the deformation to 10 cm, what level of resistance force is required? What is the deceleration of the vehicle in this condition?
c. The torsional stiffness of a cylindrical shaft of diameter D and length l is: