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A gun weighing 4 kg fires a bullet of 80 g wires a velocity of 120 m/s.With what velocity does the gun recoil?What is combined momentum of the gun and bullet before firing and after firing?
Answers
Answer:
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Explanation:
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Mass of gun, M = 10 kg
Mass of gun, M = 10 kgMass of bullet, m = 30 g = 0.03 kg
Mass of gun, M = 10 kgMass of bullet, m = 30 g = 0.03 kgVelocity of bullet, v = 330 m/s
Mass of gun, M = 10 kgMass of bullet, m = 30 g = 0.03 kgVelocity of bullet, v = 330 m/sVelocity of gun, V = ?
Mass of gun, M = 10 kgMass of bullet, m = 30 g = 0.03 kgVelocity of bullet, v = 330 m/sVelocity of gun, V = ?Momentum of the system (gun and bullet) before firing = 0
Mass of gun, M = 10 kgMass of bullet, m = 30 g = 0.03 kgVelocity of bullet, v = 330 m/sVelocity of gun, V = ?Momentum of the system (gun and bullet) before firing = 0Momentum of the system (gun and bullet) after firing = m v + MV
v + MVUsing conservation of momentum,
v + MVUsing conservation of momentum,m v + MV = 0
v + MV = 0=> 0.03 × 330 + 10V = 0
v + MV = 0=> 0.03 × 330 + 10V = 0=> V = -0.99 m/s
v + MV = 0=> 0.03 × 330 + 10V = 0=> V = -0.99 m/s(the negative sign implies direction of velocity of gun is opposite to that of the bullet)
v + MV = 0=> 0.03 × 330 + 10V = 0=> V = -0.99 m/s(the negative sign implies direction of velocity of gun is opposite to that of the bullet)Momentum of the gun after firing = MV = 10 × (-0.99) = -9.9 kg m/s
v + MV = 0=> 0.03 × 330 + 10V = 0=> V = -0.99 m/s(the negative sign implies direction of velocity of gun is opposite to that of the bullet)Momentum of the gun after firing = MV = 10 × (-0.99) = -9.9 kg m/sMomentum of the bullet after firing = mv = 0.03 × 330 = 9.9 kg m/s
v + MV = 0=> 0.03 × 330 + 10V = 0=> V = -0.99 m/s(the negative sign implies direction of velocity of gun is opposite to that of the bullet)Momentum of the gun after firing = MV = 10 × (-0.99) = -9.9 kg m/sMomentum of the bullet after firing = mv = 0.03 × 330 = 9.9 kg m/sNote that the momentum of the bullet and the gun are equal and opposite after firing.
v + MV = 0=> 0.03 × 330 + 10V = 0=> V = -0.99 m/s(the negative sign implies direction of velocity of gun is opposite to that of the bullet)Momentum of the gun after firing = MV = 10 × (-0.99) = -9.9 kg m/sMomentum of the bullet after firing = mv = 0.03 × 330 = 9.9 kg m/sNote that the momentum of the bullet and the gun are equal and opposite after firing.Before firing the gun and bullet were at rest hence no momentum before firing.
v + MV = 0=> 0.03 × 330 + 10V = 0=> V = -0.99 m/s(the negative sign implies direction of velocity of gun is opposite to that of the bullet)Momentum of the gun after firing = MV = 10 × (-0.99) = -9.9 kg m/sMomentum of the bullet after firing = mv = 0.03 × 330 = 9.9 kg m/sNote that the momentum of the bullet and the gun are equal and opposite after firing.Before firing the gun and bullet were at rest hence no momentum before firing.Both before and after firing the momentum of gun and bullet together is zero.
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