Engineering Dynamics: Find gun initial recuperator force to limit recoil

[mdemel]

1)The breech and barrel of a field gun have a total mass of 453.6kg. The recoil of the barrel is controlled by resistance forces from a buffer and recuperator, these forces are given by: Buffer force=71000/(s+1), recuperator force= P+ 4380s. (both are in Newtons). s is the recoil of the barrel. P is the initial force in the recuperator. Determine the value of P necessary to limit the recoil to 1m when a 110N projectile is fired with a muzzle velocity of 760m/s.

2) Equations used: p(before)=p(after) from conservation of momentum. Net force F=ma. a=v.dv/vs.

3) attempted solution and question with diagram is attached. There is also an answer at the bottom but i could not get it.

 

[gneill]

Think in terms of energy conservation. In the instant after the gun fires the gun will have some kinetic energy corresponding to the momentum it gained. The buffer and recuperator will do work on the gun to bring it to a halt over a distance of 1 meter.