Question

Prove that the magnitude of the ratio of difference in speed after collision to the difference in the speed before collision for a 1D elastic collision is equal to one

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

12m

1v12+12m2v'22

(two-object elastic collision)

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