Question 1 State the law of conservation of mass?

Question 2 Discuss the conservation of momentum in a rocket taking off from the ground?

Question 3 A 60 g bullet fired from a 5 kg gun leaves with a speed of 500 m/s. Find the speed with which the gun recoils?

**Conservation of Momentum**

When two or more bodies act upon one another, their total momentum remains conserved provided no external force acts on them.

For Example : When a speeding truck hit a stationary car due to which the car also start moving.

Truck | Car | |

Velocity | Decreases | Increases |

Momentum | Decreases | Increases |

The momentum lost by truck is gained by car.

Momentum can neither be created nor destroyed .

Let us consider a truck and car are moving in same direction but with different speeds.

Truck | Car | |

Mass | m_{1} |
m_{2} |

Velocity | u_{1} |
u_{2} |

Initial Momentum | m_{1}u_{1} |
m_{2}u_{2} |

Total momentum=m_{1}u_{1} + m_{2}u_{2}

Suppose the car and truck collide for a short time t, their velocities will change._{
}

Truck | Car | |

Mass | m_{1} |
m_{2} |

Velocity | v_{1} |
v_{2} |

Final Momentum | m_{1}v_{1} |
m_{2}v_{2} |

Total Momentum = m_{1}v_{1 }+ m_{2}v_{2}

Acceleration of car (a) = (v_{2 }– u_{2) }/ t _{ }

F = m x a

F_{1 }= Force exerted by truck on the car

F_{1} = m_{2} x (v_{2 }– u_{2}) / t

Acceleration of truck = (v1 – u1) / t

F_{2 } = m_{1 }x (v_{1 }– u_{1 }) / t

F_{1 }= – F_{2}

m_{2 } x (v_{2 }– u_{2 })/ t = – m_{1 }x (v_{1 }– u_{1 })/ t

m_{2} (v_{2 }– u_{2 }) = – m_{1 }* (v_{1 }– u_{1 })

m_{2 }v_{2 } – m_{2 }u_{2 } = – m_{1} v_{1 }+ m_{1} u_{1}

m_{2 }v_{2 } + m_{1} v_{1 }= m_{1} u_{1 }+ m_{2 }u_{2 }

or

m_{1} u_{1 }+ m_{2 }u_{2 } = m_{2 }v_{2 } + m_{1} v_{1}

Bibhudutta Behera says

Nice one useful

admin says

thanks