Calculating change in angle from an impulse force

[jacobh]

say there was a rifle that pivoted about the center of its butt..
if you knew the force from the bullet, the weight of the gun and its center of mass, the distance from the center of the barrel to the center of the butt, and the distance from the center of gravity and the center of the butt, how would you go about determining the maximum angle the gun raises after firing?

i'm a little stumped. i don't recall doing any problems like this back in school, so any help would be appreciated

by the way, assume that no other forces acting upon the gun (no hand holding the forearm)

 

[OlderDan]

You need to know the perpendicular distance from the line of the barrel to the point of rotation. If you know the velocity of the bullet, you can use conservation of angular momentum to get an initial angular velocity for the barrel. You need a reasonable model for the mass distribution of the barrel and stock to calculate the moment of intertia about the bivot point.

 

[jacobh]

so how can i get the maximum angle from angular velocity?

 

[OlderDan]

so how can i get the maximum angle from angular velocity?

You could use energy conservation for that. If you know the angular velocity imparted to the barrel from angular momentum conservation, the barrel will have rotational kinetic energy about the pivot point. As the CM of the barrel raises, its potential energy increases and the kinetic energy decreases. At the highest point, the kinetic energy is zero and the change in potential energy equals the initial kinetic energy. Calculate the angle from the geometry of the original and final lines of the barrel.