Question

Discuss the elastic collision of two bodies in one dimension calculate the velocity of tje bodies after the collisions

Answer 1

the elastic collision of two objects moving along the same line—a one-dimensional problem. An elastic collision is one that also conserves internal kinetic energy. Internal kinetic energy is the sum of the kinetic energies of the objects in the system. Figure 1 illustrates an elastic collision in which internal kinetic energy and momentum are conserved.

ELASTIC COLLISION

An elastic collision is one that conserves internal kinetic energy.

INTERNAL KINETIC ENERGY

Internal kinetic energy is the sum of the kinetic energies of the objects in the system.
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Now, to solve problems involving one-dimensional elastic collisions between two objects we can use the equations for conservation of momentum and conservation of internal kinetic energy. First, the equation for conservation of momentum for two objects in a one-dimensional collision is

 p1 + p2 = p′1 + p′2 (Fnet = 0)

or

m1v1 + m2v2 = m1v′1 + m2v′2 (Fnet = 0),

where the primes (′) indicate values after the collision. By definition, an elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals the sum after the collision. Thus,

12m1v12+12m2v22=12m1v'12+12m2v'22(two-object elastic collision)12m1v12+12m2v22=12m1v′12+12m2v′22(two-object elastic collision)

expresses the equation for conservation of internal kinetic energy in a one-dimensional collision.

Answer 2

Explanation:

ELASTIC COLLISION:

• Elastic collision of two moving objects is in the same direction in a one-dimensional issue.
• An elastic collision conserves both internal kinetic energy and momentum.
• The total kinetic energy of the system's objects is its internal kinetic energy. An elastic collision with conserved internal kinetic energy and momentum is shown in Figure 1.

INTERNAL KINETIC ENERGY:

• The total kinetic energy of the system's objects is its internal kinetic energy.

• Now, we may apply the equations for momentum conservation and internal kinetic energy conservation to issues involving one-dimensional elastic collisions between two objects.

• First, the equation for momentum conservation for two objects colliding in one dimension is

                        p1 + p2 = p′1 + p′2 (Fnet = 0)

or

             m1v1 + m2v2 = m1v′1 + m2v′2 (Fnet = 0),

• The values following the collision are indicated by the primes (′).
• Because an elastic collision by definition conserves internal kinetic energy, the total kinetic energy before and after the collision is equal.

Thus,

• 12m1v12+12m2v22=12m1v'12+12m2v'22(two-object elastic collision)

        12m1v12+12m2v22=12m1v′12+12m2v′22(two-object elastic collision) expresses the equation for the conservation of internal kinetic energy in a one-dimensional collision.

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