Using second law of motion, derive the relation between force and… - Vidyadip

Question

Using second law of motion, derive the relation between force and acceleration. A bullet of mass $10 g$ strikes a sand bag with a velocity of $103\ m/s^1$ and gets embedded after travelling $5 \ cm$. Calculate
$i$. the resistive force exerted by the sand bag on the bullet.
$ii.$ the time taken by the bullet to come to rest.

✓

Answer

$\text { i. } m=10 g=\frac{10}{2000} \ kg,$
$ u=10^2 m / s, v=0, s=\frac{5}{100} m$
$v^2-u^2=20 s$
$\Rightarrow 0-\left(10^3\right)^2=2 \cdot a \cdot \frac{s}{100}$
$\Rightarrow a=\frac{1000-1000}{2 \times 5} \times 100$
$--10^7 ms^2$
$\Rightarrow F=ma=-10^5 N$
$ii. v=u+a t$
$=0=\left(10^7\right) \cdot 10^7 t$
$\Rightarrow 10^7 t=10^3$
$\Rightarrow t=\frac{10^2}{10^7}-10^{-4}s$

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