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Derive the mathematical formula of conservation of momentum.​

User Mosh Feu
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Step-by-step explanation:

  • To explain conservation of momentum, let us take the following example. Consider two balls A and B having masses ml andm, respectively. Let the initial velocity of ball A be u1, and that of ball B be u2 (u1 > u2). Their collision takes place for a very short interval of time t and after that A and B start moving with velocities v1 and v2 (now v1 < v2)
User Mali Remorker
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Let's start by defining momentum. Momentum (p) is defined as the product of an object's mass (m) and its velocity (v):

p = m x v

The total momentum of a system of objects is simply the sum of the momenta of all the objects in the system:


p_{total = p_1 + p_2 + ... + p_n

Now, let's consider two objects in a system, labeled 1 and 2. If there are no external forces acting on the system, the total momentum of the system remains constant:


p_{total = p1__i + p2_i = p1_f + p2_f

where p1_i and p2_i are the initial momenta of objects 1 and 2, respectively, and p1_f and p2_f are the final momenta of objects 1 and 2, respectively.

If we express the momenta in terms of mass and velocity, we get:

m1v1_i + m2v2_i = m1v1_f + m2v2_f

This is the mathematical formula of conservation of momentum. It states that the sum of the products of mass and velocity before a collision is equal to the sum of the products of mass and velocity after a collision, provided that no external forces act on the system.

User Moh Tarvirdi
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