Question

For a ballistic study, a 2.4 - gm bullet is fired into soft wood. The bullet strikes the wood surface with a velocity of 358 m/s and penetrates 0.19 m. Find the constant retarding force in N. Include the sign (+ or -) if the unknown variable is a vector quantity.

Answer 1

We can find the constant retarding force from the work-kinetic energy theorem:

$$\Delta KE=W,$$ $$KE_f-KE_i=Fd,$$ $$0-\dfrac{1}{2}mv_i^2=Fd,$$ $$F=\dfrac{-\dfrac{1}{2}mv_i^2}{d},$$ $$F=\dfrac{-\dfrac{1}{2}\cdot2.4\cdot10^{-3}\ kg\cdot(358\ \dfrac{m}{s})^2}{0.19\ m}=-809.46\ N.$$

The sign minus means that the constant retarding force acts in the opposite direction to the motion of the bullet.