I don't quite follow. With a given force and impulse (duration of that force), don't heaver things accelerate more slowly?
A rifle mounted rigidly to a concrete wall would make the total mass very high so the average rearward acceleration would be small...
I am not too knowledgeable about vibrating stuff or this high force/short impulse. Are you explaining that a rigidly held rifle will vibrate more violently then a padded one? By vibrating violently, parts of it will have high instantaneous acceleration?
Is vibration/metal flexibility more of a problem in a rifle or the average reward recoil from driving the bullet (a la conservation of momentum) ?
thanks in advance!
Happy to respond... I recognize an open mind when I see one. Pardon me if I stray from a purely academic explanation.
First off, I think I introduced some error by mixing up mass with stiffness.
Heavier and
stiffer are two different things.
Consider the case of a cannon ball being dropped from a given height onto first, a thick steel plate, and second, onto a big rubber ball. In each case, the force of the cannon ball imparted onto the target is the same - F = ma, the mass of the cannon ball times the acceleration due to gravity. Let's say the steel plate weighs the same as the rubber ball. But what differs in each case is the duration of the impact event. If you had a load cell under each target, the cannon ball hitting the steel plate would have a very high measured force, but with a very small time duration. Conversely, the impact on the big rubber ball would have a lower peak force but the impact event would take place over a much longer time period. In each case, the impulse (F*dt, or integral of force over time) would be nearly the same.
Now let's interject that momentum is the product of mass and velocity, and it bears the same units as impulse, the product of force and time.
Back to my misguidance - since the mass of the targets in my cannonball example are the same (by definition), and the force of impact is the same, what varies between the two cases is acceleration and time. To arrive at the same momentum, if one has a longer duration (the 'soft' target, the rubber ball) is must have a lower acceleration, and likewise, the steel plate will have a shorter duration and a much higher acceleration.
Are you explaining that a rigidly held rifle will vibrate more violently then a padded one? By vibrating violently, parts of it will have high instantaneous acceleration?
Yes. What is different is that the duration of the equal and opposite reaction will differ, depending on the elasticity (stiffness) of the system against which the bullet's firing is being reacted. High stiffness, short duration; low stiffness, long duration.
Is vibration/metal flexibility more of a problem in a rifle or the average reward recoil from driving the bullet (a la conservation of momentum) ?
Momentum is of course being conserved. m1V1 = m2 V2, so if m2 is a lot bigger than m1, V2 will be a lot lower than V1. But what needs to enter into the equation is the duration of each event; in the initial event, the firing of the bullet takes place over a very short period and imparts a huge acceleration to a small mass. The reaction takes place against a larger mass, and the duration of the reaction depends on the stiffness of the system being reacted against.
An even simpler model would be to consider a rifle hung by two threads. The gun fires, and the gun recoils over a certain period of time and it swings backward a certain distance. Double the weight of the rifle, and the distance it recoils will be less than for the unweighted gun.
Now take the same model, but this time there is a coil spring between the butt of the gun and a solid wall. When the gun fires, the recoil is reacted by the combined stiffness of the spring and the solid wall. Now vary the stiffness of that coil spring... the mass hasn't changed, the recoil force and momentum haven't changed... but the acceleration and the velocity have changed.
Does that make sense, or have I added more confusion?
