Question

A bullet of mass 50 g moving with an initial velocity of 100 m/s, strikes a wooden block and comes to rest after penetrating a distance of 2 cm in it. Calculate the retardation caused by the wooden block.

Answer 1

A bullet of mass $50\,\mathrm{g}$ moving with an initial velocity of $100\,\mathrm{m/s}$, strikes a wooden block and comes to rest after penetrating a distance of $2\,\mathrm{cm}$ in it. Calculate the retardation caused by the wooden block.

Coordinate for uniformly accelerated motion equals:

$$l = v_0 t - \frac{a t^2}{2}$$

$v_0$ - initial velocity of the bullet

$a$ - deceleration

$t$ - time

Velocity for uniformly accelerated motion equals:

$$v = v_0 - a t$$

If bullet comes to rest: $v = 0 \Rightarrow t = \frac{v_0}{a}$

Therefore, from the equation for coordinate:

$$l = v_0 \frac{v_0}{a} - \frac{a \left(\frac{v_0}{a}\right)^2}{2} = \frac{v_0^2}{2a}$$

deceleration equals:

$$a = \frac{v_0^2}{2l} = \left(100 \frac{m}{s}\right)^2 / 2$$

And, finally, retardation equals:

$$F = m a = m \frac{v_0^2}{2l} = 0.05\,kg \cdot \frac{\left(100 \frac{m}{s}\right)^2}{2 \cdot 0.02\,m} = 12500\,N = 12.5\,kN$$

Answer: 12500 N