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 Ex: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}

_{ }

v_{2 }– u_{2}

Acceleration of car (a) = ————-

t

F = m * a

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

F_{1} = m_{2 * }(v_{2 }– u_{2})

———————

t

v_{1} – u_{1 }

Acceleration of truck =————

t

F_{2 } = m_{1} * (v_{1 }– u_{1 })

———————

t

F_{1 }= – F_{2}

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

——————– = —————–

t 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