Answer to Question #161467 in Mechanical Engineering for Shakir

Question

) A gun barrel weight 300 kg and has a recoil spring of

stiffness 250N/mm. The barrel recoils 0.8m on firing.

Determine the (i) Critical recoil velocity of the gun,

(ii) Critical damping coefficient of the dashpot engaged

at the end of the recoil stroke.

Answer 1

natural frequency

𝜔 = $\sqrt \frac{𝑘}{𝑚}$

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

= 28.867𝑟𝑎𝑑/𝑠 .

From conservation of energy,

$\frac{𝑚𝑣2}{2} = \frac{kx2}{2}$

𝑣 = 𝜔𝑥

= (28.867)(0.8)

= 23.09396 𝑚/ 𝑠 .