Question

A bullet with a mass of m = 17 g is shot out of a rifle that has length L = 1.16 m. The bullet spends t = 0.12 s in the barrel. find the acceleration and net force?

Answer 1

Answer:

a = 161.11 m/s²

Fnet = 2.74 N

Explanation:

We know the distance traveled L = 1.16m and the time t = 0.12s, additionally, the initial velocity is vi = 0 m/s, so we can use the following equation to find the acceleration:

$\begin{gathered} x_f=x_i+v_it+\frac{1}{2}at^2 \\ x_f-x_i=v_it+\frac{1}{2}at^2 \\ L=v_it+\frac{1}{2}at^2 \end{gathered}$

Replacing the values and solving for a, we get:

$\begin{gathered} 1.16=0(0.12)+\frac{1}{2}a(0.12)^2_{} \\ 1.16=0+\frac{1}{2}(0.144)a \\ 1.16=0.0072a \\ \frac{1.16}{0.0072}=a \\ 161.11m/s^2=a \end{gathered}$

Then, the net force is equal to the mass times acceleration, so:

$\begin{gathered} F_{\text{net}}=ma \\ F_{\text{net}}=0.017\operatorname{kg}(161.11m/s^2) \\ F_{\text{net}}=2.74\text{ N} \end{gathered}$

So, the answers are:

a = 161.11 m/s²

Fnet = 2.74 N