Question

Currently, eighty-five percent of all neck injuries are caused by rear-end car collisions. To alleviate this problem, an automobile seat restraint has been developed that provides additional pressure contact with the cranium. During dynamic tests, the distribution of load on the cranium has been plotted and shown to be parabolic. Determine the equivalent resultant force and its location, measured from point A. 

• A. \( F_R = 7 \text{ lb}, \quad x = 0.268 \text{ ft} \)
• B. \( F_R = 5 \text{ lb}, \quad x = 0.223 \text{ ft} \)
• C. \( F_R = 12 \text{ lb}, \quad x = 0.718 \text{ ft} \)
• D. \( F_R = 4 \text{ lb}, \quad x = 0.482 \text{ ft} \)

Hint:

- Use centroid method for distributed forces. - Parabolic loads have resultant force at \( x = \frac{3}{8}L \).

Answer 1

The Correct Option is A

- For parabolic load distributions, the resultant force is given by: \[ F_R = \int_0^L w(x) \, dx \] - The location of the resultant force is determined using centroid formulas.