Question

State it by the expression for conservation of momentum

Answer 1

conservation of momentum

Answer 2

Conservation of Momentum

We know that moving bodies posses momentum which is equal to the product of mass and velocity. That is,

Momentum = mass × velocity

According to the law of conservation of momentum: When two or more bodies act upon one another, their total momentum remains constant or conserved provided no external forces are acting.

The law of conservation of momentum means that whenever 1 body gains momentum, then some other body must lose an equal amount of momentum.

Suppose that during collision, the truck exerts a force F₁ on the car and, in turn, the car exerts a force F₂ on the truck. will now find out the values of forces F₁ and F₂.

(i) When the force F₁ off the track apps upon the car for a time t, then the velocity of the car changes from u₂ to v₂. So,

Acceleration of car, a₂ = (v₂ - u₂)/t

But, force = mass × acceleration, so the force F₁ exerted by the truck on the car is given by :

F₁ = m₂ × (v₂ - u₂)/t __________(1)

(ii) When the force of F₂ of the car reacts on the truck for a time t, then the velocity of the track changes from u₁ to v₁. So,

Acceleration of truck, a₁ = (v₁ - u₁)/t

But, force = mass × acceleration, so the force F₂ exerted by car on the truck is given by:

F₂ = m₁ × (v₁ - u₁)/t ___________(2)

Now, the force F₁ exerted by the truck is the ‘action' and force F₂ exerted by the car is the ‘reaction'. But according to the third law of motion, the action and 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

or, m₂v₂ - m₂u₂ = -m₁v₁ + m₁u₁

or, m₂v₂ + m₁v₁ = m₂u₂ + m₁u₁

or, m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Now, m₁u₁ + m₂u₂ represents total momentum of the truck and car before collision whereas m₁v₁ + m₂v₂ represents the total momentum of the truck and car after collision. This means that:

Total momentum before collision = Total momentum after collision.

it is obvious that the total momentum of the two bodies before and after the collision is the same. This means that momentum of the two bodies remains constant. This results prove the law of conservation of momentum.