Two identicalls bullets are fired one by a light rifle and the other by a heavier rifle with the same force. Which rifle will hurt the should more and why?
Two identical bullets each say of 'm’ kg are fired from two different rifles one a light one of M kg and second heavier of mass M' kg. Since the bullets are identical, let them leave the velocity V m/s.
Momentum of the bullet before firing = 0 kg-m/s (as bullet is stationary)
Momentum of the rifle before firing= 0 kg-m/s ( as the rifle is stationary)
Momentum of the bullet- rifle system before furing= 0 kg-m/s
Momentum of the bullet after it is fired = m× V kg-m/s.
As the momentum of the rifle bullet system needs to be conserved, so the rifle recoils, let it recoil with a velocity v (in case of the light rifle).
Recoil momentum of the light rifle= -M v kg-m/s( negative sign as the recoil velocity is in a direction opposite to the bullet velocity).
Combined momentum of the rifle and bullet after firing = Momentum of the bullet + momentum of the rifle= (m V - M v) kg-m/s
Conservation of momentum before and after firing the bullet requires;
m V - M v= 0; ===========> v = recoil velocity of rifle= (m V/M).–––––––––––––––––––––––(1)
Let the recoil velocity of heavier gun be v' m/s. A similar analysis gives;
Momentum of rifle and bullet before firing= 0 kg-m/s
Momentum of bullet after firing = m V kg-m/s
Momentum of heavier rifle after firing=- M' v'kg-m/s
Conservation of momentum of the system requires that;
m V - M' v' = 0 ; ===> v' = recoil velocity of heavier rifle = (m V/M') ––––––––––––––––––––––(2)
(Recoil velocity of lighter rifle v m/s ÷ Recoil velocity of heavier rifle v' m/s) = M'/M.
Since M' > M, so lighter rifle will recoil with more velocity than the heavier rifle and hurt the shoulder more.
Two identical bullets each say of 'm’ kg are fired from two different rifles one a light one of M kg and second heavier of mass M' kg. Since the bullets are identical, let them leave the velocity V m/s.
Momentum of the bullet before firing = 0 kg-m/s (as bullet is stationary)
Momentum of the rifle before firing= 0 kg-m/s ( as the rifle is stationary)
Momentum of the bullet- rifle system before furing= 0 kg-m/s
Momentum of the bullet after it is fired = m× V kg-m/s.
As the momentum of the rifle bullet system needs to be conserved, so the rifle recoils, let it recoil with a velocity v (in case of the light rifle).
Recoil momentum of the light rifle= -M v kg-m/s( negative sign as the recoil velocity is in a direction opposite to the bullet velocity).
Combined momentum of the rifle and bullet after firing = Momentum of the bullet + momentum of the rifle= (m V - M v) kg-m/s
Conservation of momentum before and after firing the bullet requires;
m V - M v= 0; ===========> v = recoil velocity of rifle= (m V/M).–––––––––––––––––––––––(1)
Let the recoil velocity of heavier gun be v' m/s. A similar analysis gives;
Momentum of rifle and bullet before firing= 0 kg-m/s
Momentum of bullet after firing = m V kg-m/s
Momentum of heavier rifle after firing=- M' v'kg-m/s
Conservation of momentum of the system requires that;
m V - M' v' = 0 ; ===> v' = recoil velocity of heavier rifle = (m V/M') ––––––––––––––––––––––(2)
(Recoil velocity of lighter rifle v m/s ÷ Recoil velocity of heavier rifle v' m/s) = M'/M.
Since M' > M, so lighter rifle will recoil with more velocity than the heavier rifle and hurt the shoulder more.
