Question

Automobiles must be able to sustain 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 (v = 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 v = 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 deacceleration of the vehicle in this condition?

Answer 1

Step-by-step explanation:

The concept of Hooke's law was applied as it relates to deformation.

The detailed steps and appropriate substitution is as shown in the attached file.