# what is the basic concept of coservation of momentum?

### Asked by Akshya Achu | 21st Aug, 2014, 08:13: PM

### 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 *m*_{A} and *m*_{B} initially moving in a straight line with velocities *u*_{A} and *u*_{B}, respectively. Assume that *u*_{A} > *u*_{B}. They collide with each other as shown below. The total momentum of the two objects before collision is m_{A}u_{A}+m_{B}u_{B}.

The collision lasts for time *t*. During this collision, A exerts a force *F*_{AB} on B and B exerts a force *F*_{BA} on A.Suppose *v*_{A} and *v*_{B} are the velocities of A and B after collision, the momentum before and after collision for object A is *m*_{A}*u*_{A} and *m*_{A}*v*_{A} respectively. Thus, according to Newton's law, the force *F*_{AB} can be written as :

* *Similarly_{,}* *the force *F*_{BA} on A is:

According to the third law of motion, we have :

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.

**p = m v**

*m*

_{A}and

*m*

_{B}initially moving in a straight line with velocities

*u*

_{A}and

*u*

_{B}, respectively. Assume that

*u*

_{A}>

*u*

_{B}. They collide with each other as shown below. The total momentum of the two objects before collision is m

_{A}u

_{A}+m

_{B}u

_{B}.

The collision lasts for time *t*. During this collision, A exerts a force *F*_{AB} on B and B exerts a force *F*_{BA} on A.Suppose *v*_{A} and *v*_{B} are the velocities of A and B after collision, the momentum before and after collision for object A is *m*_{A}*u*_{A} and *m*_{A}*v*_{A} respectively. Thus, according to Newton's law, the force *F*_{AB} can be written as :

* *Similarly_{,}* *the force *F*_{BA} on A is:

According to the third law of motion, we have :

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 | 22nd Aug, 2014, 09:18: AM

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