Answer to Question #161485 in Mechanical Engineering for Ganesh Sen

Question

a gun barrel weight 300 kg and has a recoil spring of stiffness 250 Newton per mm the barrel is equal to 0.8m on firing determine i the critical recoil velocity of the gun .

Answer 1

(i) The natural frequency is

𝜔 = $\sqrt \frac{𝑘 }{𝑚 }$

= $\sqrt \frac{250000}{300}$

=28.87 𝑟𝑎𝑑/𝑠 .

From conservation of energy, we have

$\frac{ 𝑚𝑣2}{2}$ = $\frac{𝑘𝑥2}{2 }$

𝑣 = 𝜔𝑥 = (28.87)(0.8)

=23.096𝑚/𝑠 .