Question

Prove for elastic collision the velocity of approach is always equal to the velocity of recession

Answer 1

Answer:

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,

1

2

m

1

v

1

2

+

1

2

m

2

v

2

2

=

1

2

m

1

v

'

1

2

+

1

2

m

2

v

'

2

2

(

two-object elastic collision

)

expresses the equation for conservation of internal kinetic energy in a one-dimensiona