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what is the basic concept of coservation of momentum?
Asked by Akshya Achu | 21 Aug, 2014, 08:13: PM
answered-by-expert Expert Answer
According to the second law of motion we know that moving bodies possess momentum and is equal to the product of mass and velocity.
                                    p = m v
According to the law of conservation of momentum " When two or more bodies act upon one another, their total momentum remains constant provided no external force are acting."
Consider a collision between a moving and a stationary object. When the collision occurs, the velocity of the moving object decreases, but at the same time, the velocity of the stationary object increases.Due to this the momentum of moving object decreses and the momentum of the stationary object increases.The increase in the momentum of the stationary object is equal to the decrease in the momentum of the moving object.Thus there is no loss of momentum during collision.
Thus, the law of conservation of momentum can be stated as the sum of momenta of objects before collision is equal to the sum of momenta after collision, provided there is no external force acting on the objects.
 
Consider two objects A and B of masses mA and mB initially moving in a straight line with velocities uA and uB, respectively. Assume that uA > uB. They collide with each other as shown below. The total momentum of the two objects before collision is mAuA+mBuB.

 

 

 The collision lasts for time t. During this collision, A exerts a force FAB on B and B exerts a force FBA on A.Suppose vA and vB are the velocities of A and B after collision, the momentum before and after collision for object A is mAuA and mAvA respectively. Thus, according to Newton's law, the force FAB  can be written as :

                              Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.

 Similarly, the force FBA on A is:

                             Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.

According to the third law of motion, we have :

Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.

 i.e The total momentum of both objects A and B before collision is equal to the total momentum of both objects after collision.

Thus, the momentum is conserved in a collision.

Answered by Jyothi Nair | 22 Aug, 2014, 09:18: AM

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