- Linear Momentum
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- Impulse and Momentum
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- Conservation of Linear momentum
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- Recoil of the Gun
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- Motion of the system with varying mass(Rocket)
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- Linear Momentum Problems with Solutions

- Consider the gun and bullet in its barrel as an isolated system

- In the beginning when bullet is not fired both the gun and bullet are at rest.So the momentum of the before firing is zero

p_{i}=0

- Now when the bullet is fired ,it moves in the forward direction and gun recoil back in the opposite direction

- Let m
_{b}be the mass and v_{b}of velocity of the bullet And m_{g}and v_{g}be the velocity of the gun after the firing

- Total momentum of the system after the firing would be
p

_{f}=m_{b}v_{b}+m_{g}v_{g}

- since no external force are acting on the system,we can apply the law of conservation of linear momentum to the system

Therefore

$p_{final}=p_{initial}$

or $m_bv_b +m_gv_g=0$

or $v_g=-\frac {m_bv_b}{m_g}$

- The negative sign in above equation shows that velocity of the recoil of gun is opposite to the velocity of the bullet

- Since mass of the gun is very large as compared to the mass of the bullet,the velocity of the recoil is very small as compared to the velocity of the bullet

Calculate the recoil velocity of gun whose mass is 5 kg and it shoot the bullet of mass .015 kg with velocity 500 m/s

$v_g=-\frac {m_bv_b}{m_g}$

Here $m_b=.015 kg$

$v_b=500 m/s$

$m_g=5 Kg$

So ,

$v_g=-\frac {.015 \times 500}{5}=-1.5 m/s$

Here $m_b=.015 kg$

Class 11 Maths Class 11 Physics Class 11 Chemistry