20DQ - University Physics with Modern Physics

Question

Why are cars designed to crumple in front and back for safety? Why not for side collisions and rollovers?

Step-by-Step Solution

Answer

The crumpling at the front and back reduces the change in momentum, i.e., time t is made larger to decrease the force of impact.

Step 1: Newton’s Second law

A body accelerates when a net force acts on it and travels in the same direction as the net force. The product of mass and acceleration vector is equal to the force vector.

$\sum \overrightarrow{\mathrm{F}}=\mathrm{m}\overrightarrow{\mathrm{a}}$

Step 2: Kinematic equation in terms of acceleration, velocity, and initial velocity

The force acted on the body at the end of the collision will depend on the de-acceleration, and the time it took to stop the car completely.

$\begin{array}{rcl}\mathrm{F}& =& \mathrm{ma}\\ & =& \mathrm{m}\left(\frac{\mathrm{v}-\mathrm{u}}{\mathrm{t}}\right)\\ & =& \mathrm{m}\left(\frac{0-\mathrm{u}}{\mathrm{t}}\right)\\ & =& -\frac{\mathrm{mu}}{\mathrm{t}}\end{array}$

The crumpling at the front and back reduces the change in momentum, i.e., time t is made larger to decrease the force of impact. One of the reasons the car is not designed to crumple on the sides is that statistically, most of these accidents happen at the front or the back, so it makes sense if it is made for the front and back. Another reason is design; there is no space to make a crumple zone on the sides. Making crumple zones on the sides will take too much space.

Thus, the crumpling at the front and back reduces the change in momentum, i.e., time t is made larger to decrease the force of impact.