Question

collision derivation​

Answer 1

In all collisional interactions momentum remain conserved. Collisions are called elastic collisions if, in addition to momentum conservation, kinetic energy remain conserved too. To derive the elastic collision equations we make use of the Momentum Conservation condition and Kinetic Energy Conservation condition.

m

1

- Mass of object 1;

m

2

- Mass of object 2;

v

1

i

- velocity of object 1 before collision;

v

2

i

- velocity of object 2 before collision;

v

1

f

- velocity of object 1 after collision;

v

2

f

- velocity of object 2 after collision;

Momentum Conservation:

m

1

v

1

i

+

m

2

v

2

i

=

m

1

v

1

f

+

m

2

v

2

f

Rearrange this by bring all therms with

m

1

on one side and terms with

m

2

on the other side,

m

1

(

v

1

i

−

v

1

f

)

=

m

2

(

v

2

f

−

v

2

i

)

............... ( 1 )

m

1

(

v

1

i

−

v

1

f

)

m

2

(

v

2

f

−

v

2

i

)

=

1

........... ( 2 )