Question

A bullet of mass 0.5kg has a speed of 400m/s at what energy does it more? If hits the wall of which the average resistance force is 10,000N. Calculate the distance penetrated by the bullet.

Answer 1

We apply the kinetic energy change theorem

$A= \frac{m\cdot v^2}{2}-\frac{m\cdot v_0^2}{2}=\frac{m\cdot 0}{2}-\frac{m\cdot v_0^2}{2}=-\frac{m\cdot v_0^2}{2}$

A is the work of the power of resistance. It is defined as the scalar product of the vector of the force itself and the displacement vector.

Since they are directed in opposite directions (the angle between them is 180 °), then:

$A=F \cdot S\cdot \cos(180^0)=-F \cdot S$

then we get

$-F \cdot S=-\frac{m\cdot v_0^2}{2}$

where from

$S=\frac{m\cdot v_0^2}{2 \cdot F}=\frac{0.5(kg)\cdot 400^2(\frac{m^2}{s^2})}{2 \cdot 10000(N)}=4(m)$