Question

A rifle with a weight of 25 N fires a 4.0 g bullet with a speed of 290 m/s.

(a) Find the recoil speed of the rifle.
Your response is off by a multiple of ten. m/s
(b) If a 750 N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle.
m/s

Answer 1

Step-by-step explanation:

Given

Weight of rifle
`W=25\ N`

mass of rifle
`M=(25)/(10)=2.5\ kg`

mass of bullet
`m=4\ gm`

speed of bullet
`u=290\ m/s`

As there is no net force on the bullet-rifle system therefore momentum is conserved

`0=Mv+mu`

`v=-(mu)/(M)`

`v=-(4* 10^(-3)* 290)/(2.5)`

`v=-0.464\ m/s`

i.e. opposite to the direction of bullet speed

(b)Weight of Man
`=750\ N`

Combined weight of man and rifle
`=750+25=775\ N`

mass of man-rifle system
`M'=(775)/(10)=77.5\ kg`

Now man and rifle combinedly recoil

therefore

`0=(M')v '+mu`

`v'=-(mu)/(M')`

`v'=-(4* 10^(-3)* 290)/(77.5)`

`v'=0.0149\ m/s`