Question

calculate the velocity of two bodies after elastic collision in 1 dimensions ​

Answer 1

Answer:

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.

....

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.

Explanation: