Question

From a rifle of mass 5kg, a bullet of mass 50gram is fired with an initial velocity of 50m/s. Calculate the initial recoil velocity of the rifle.

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Answer 1

you know about \text{\underline{conservation of linear momentum}}

conservation of linear momentum

when external force act on system = 0 , linear momentum of system remains constant.

I mean, initial momentum = final momentum

here mass of rifle , M = 5Kg

mass of bullet , m = 50gm = 0.05kg

initial velocity of bullet , u = 50 m/s

we have to find initial recoil velocity of rifle , U

final velocity of bullet , v = 0

final velocity of rifle , V = 0

use conservation of linear momentum,

mu+MU=mv+MVmu+MU=mv+MV

0.05 × 50 + 5 × U = m × 0 + M × 0

0.05 × 50 + 5U = 0

5U = -0.05 × 50

U = -0.5 m/s [here negative sign shows that velocity of rifle is just opposite to the bullet . yes of course it is recoil velocity ]

hence, initial velocity of refile is -0.5 m/s

Answer 2

Mass of the rifle (m1) = 4 kg

Mass of the bullet (m2) = 50 g = 0.05 kg

Recoil velocity of the rifle = v1

A bullet is fired with an initial velocity (v2) = 35 m/s

Find out

The initial recoil velocity of the rifle.

Solution

Initially, the rifle is at rest.

Thus, its initial velocity (v) = 0

The total initial momentum of the rifle and bullet system

⇒ (m1+m2) × v = 0

The total momentum of the rifle and bullet system after firing

= m1v1 + m2v2

= (4 × v1 ) + (0.05 × 35)

= 4v1 + 1.75

According to the law of conservation of momentum

Total momentum after the firing = Total momentum before the firing

4v1 + 1.75 = 0

v1= -1.75 / 4

v1 = – 0.4375 m/s

The negative sign indicates that the rifle recoils backwards with a velocity of 0.4375 m/s.

BTW HRU

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