Answer to Question #214178 in Physics for ...

Question

A bullet of mass 10 kg is fired into a block of wood with a velocity of 1 km/s. Find the 

constant retarding force on the bullet if it penetrates the block 12 cm, assuming the 

deceleration to be constant.

Answer 1

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

$$KE_f-KE_i=W,$$ $$\dfrac{1}{2}mv_f^2-\dfrac{1}{2}mv_i^2=-F_{fr}d,$$ $$0-\dfrac{1}{2}mv_i^2=-F_{fr}d,$$ $$F_{fr}=\dfrac{\dfrac{1}{2}mv_i^2}{d}=\dfrac{\dfrac{1}{2}\cdot10\ kg\cdot(1000\ \dfrac{m}{s})^2}{0.12\ m}=4.2\cdot10^7\ N.$$