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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

Respuesta :

Answer:

Explanation:

Given

Weight of rifle [tex]W=25\ N[/tex]

mass of rifle [tex]M=\frac{25}{10}=2.5\ kg[/tex]

mass of bullet [tex]m=4\ gm[/tex]

speed of bullet [tex]u=290\ m/s[/tex]

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

[tex]0=Mv+mu[/tex]

[tex]v=-\frac{mu}{M}[/tex]

[tex]v=-\frac{4\times 10^{-3}\times 290}{2.5}[/tex]

[tex]v=-0.464\ m/s[/tex]

i.e. opposite to the direction of bullet speed

(b)Weight of Man [tex]=750\ N[/tex]

Combined weight of man and rifle[tex]=750+25=775\ N[/tex]

mass of man-rifle system [tex]M'=\frac{775}{10}=77.5\ kg[/tex]

Now man and rifle combinedly recoil

therefore

[tex]0=(M')v '+mu [/tex]

[tex]v'=-\frac{mu}{M'}[/tex]

[tex]v'=-\frac{4\times 10^{-3}\times 290}{77.5}[/tex]

[tex]v'=0.0149\ m/s[/tex]

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