please explain me about liner ,momrntum conservation principle
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The principle of conservation of momentum states that the total momentum of an isolated system before the collision remains the same after the collision.
For example, take a system of two balls of mass M and m moving with velocity V and v respectively in a straight line. The total momentum of the system is (MV+mv). Let the two balls collide with each other and their final velocities becomes V₁ and v₁. After the collision, the momentum of the system is (MV₁+mv₁). Then, according to the principle of the conservation of linear momentum, (MV+mv = MV₁+mv₁)
For example, take a system of two balls of mass M and m moving with velocity V and v respectively in a straight line. The total momentum of the system is (MV+mv). Let the two balls collide with each other and their final velocities becomes V₁ and v₁. After the collision, the momentum of the system is (MV₁+mv₁). Then, according to the principle of the conservation of linear momentum, (MV+mv = MV₁+mv₁)
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For example, during a collision a truck exerts a force F₁ on the carand in turn the car exerts a force F₂ on the truck. We will now find out the values of the forces F₁ and F₂
(i)When the force F₁ of the truck acts on the car for a time t,then the velocity of car changes from u₂ to v₂. So,
Acceleration of the car, a₂=(v₂-u₂)/t
But force=mass x acceleration, so the force F₁ exerted by the truck on the car is given by:
F₁=m₂ x (v₂-u₂)/t..................(1)
(i)When the force F₂ of the car acts on the truck for a time t,then the velocity of car changes from u₁ to v₁. So,
Acceleration of the car, a₁=(v₁-u₁)/t
But force=mass x acceleration, so the force F₂ exerted by the truck on the car is given by:
F₂=m₁ x (v₁-u₁)/t...................(2)
Now the force F₁ exerted by the truck is the áction'and the force F₂ exerted by the car is the 'reaction'. But according to Newton's third law of motion, the action and the reaction are equal and opposite. That is,
F₁=-F₂
Now putting the values of F₁ and F₂ from equations (1) and (2) we get :
m₂(v₂-u₂)/t=-m₁(v₁-u₁)/t
Cancelling t from both the sides we get,
m₂(v₂-u₂)=-m₁(v₁-u₁)
m₂v₂-m₂u₂=-m₁v₁+m₁u₁
m₂v₂+m₁v₁=m₂u₂+m₁u₁
Now, m₂u₂+m₁u₁ represents the total speed of the car and the truck before the collisions whereas m₂v₂+m₁v₁ represents the total momentum after the collision of the truck and the car. This means that:
Total momentum after the collision=Total momentum before the collision
This is known as the principle of conservation of linear momentum.
(i)When the force F₁ of the truck acts on the car for a time t,then the velocity of car changes from u₂ to v₂. So,
Acceleration of the car, a₂=(v₂-u₂)/t
But force=mass x acceleration, so the force F₁ exerted by the truck on the car is given by:
F₁=m₂ x (v₂-u₂)/t..................(1)
(i)When the force F₂ of the car acts on the truck for a time t,then the velocity of car changes from u₁ to v₁. So,
Acceleration of the car, a₁=(v₁-u₁)/t
But force=mass x acceleration, so the force F₂ exerted by the truck on the car is given by:
F₂=m₁ x (v₁-u₁)/t...................(2)
Now the force F₁ exerted by the truck is the áction'and the force F₂ exerted by the car is the 'reaction'. But according to Newton's third law of motion, the action and the reaction are equal and opposite. That is,
F₁=-F₂
Now putting the values of F₁ and F₂ from equations (1) and (2) we get :
m₂(v₂-u₂)/t=-m₁(v₁-u₁)/t
Cancelling t from both the sides we get,
m₂(v₂-u₂)=-m₁(v₁-u₁)
m₂v₂-m₂u₂=-m₁v₁+m₁u₁
m₂v₂+m₁v₁=m₂u₂+m₁u₁
Now, m₂u₂+m₁u₁ represents the total speed of the car and the truck before the collisions whereas m₂v₂+m₁v₁ represents the total momentum after the collision of the truck and the car. This means that:
Total momentum after the collision=Total momentum before the collision
This is known as the principle of conservation of linear momentum.
this is a complicated , long way of explaining simple concept. but it correct.
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