Question

7. Figure 4 shows a cannon. When the gun is fired, high pressure gasses accelerate the projectile. The reaction force pushes the gun barrel in the opposite direction to the projectile. The gun barrel is made to translate backwards against a critically damped spring-damper system called the recoil mechanism. The mass of the gun barrel the recoi mechanism is 500 kg and the recoil spring stiffness is 10 kN/m. Upon firing, the gun recoils 0.4 m. Find (a) the damping coefficient of the damper (b) the initial recoil velocity of the gun (c) the time taken by the gun barrel to return to a position 0.1 m from its initial position Projectile Cum barrel Recoil mechanism spring and damper) Figure 4 Ans: 4472.1 rad/s (711.8 Hz), 4.8626 m/s, 0.8258 seconds

Answer 1

It is given that system is critically damped (a) Damping coefficient of the damper, C = (= 2 mon + what x-10 kN/m2 m= 500kg. / c=25 km C-2 51000) (500) Te = 4472.1359 rad

(6) Position Response of a critically damped systens; paritet)= C, +6 +) 2017 et (Gwo) – ungt wat w Velocity ac (A)= Now let @ t= tx=0 0= [((2-wr() - un lat,] into 7,- (2-wn C, wel when; at t=o. x = 6,=0 Now, a t=t, ,x=xman .: x=((,+Gtle wat 0.4=(Ott,) e wat 0.4 = (a t. G= 0.4w, e x= [ 0.4one - 0.4 whet] e re at t=0 % = 0.4 Une = 0.4 10000 xe V S2000

bo - 4,8656 (c) 2U Time taken by the gun barrel to return to a position Olm from it's initial position x= Gt èwnt = 0.4 whe te wasta 0.1 0.4 (1000. e tae sol ning, (to = 0.82586