Question

objects A,B,C with masses m,2 m,and m are kept on a friction less horizontal surface. The object A move towards B with a speed of 9 m/s and makes an elastic collision with it . B makes completely inelastic collision with C. Then velocity of C is?

Answer 1

With a completely elastic collision, it can be assumed that all the kinetic energy is transferred from the moving body to the body at rest.

`1/2m_"initial"v^2 = 1/2m_"other" v_"final"^2`

`1/2m(9)^2 = 1/2(2m)v_"final"^2`

`81/2 = v_"final"^2`

`sqrt(81)/2 = v_"final"`

`v_"final" = 9/sqrt(2)`

Now in a completely inelastic collision, all kinetic energy is lost, but momentum is transferred. Therefore

`m_"initial"v = m_"final"v_"final"`

`2m9/sqrt(2) = m v_"final"`

`2(9/sqrt(2)) = v_"final"`

Thus the final velocity of `C` is approximately `12.7` m/s.

Hopefully this helps!

Answer 2

`4` [m/s]

Explanation:

The collision history can be described as

1) Ellastic collision

#{(m v_0 = m v_1 + 2m v_2), (1/2m v_0^2= 1/2 m v_1^2+1/2(2m)v_2^2):}#

solving for `v_1, v_2` gives

`v_1 = -v_0/3, v_2 = 2/3 v_0`

2) Inelastic collision

`2m v_2 = (2m + m)v_3`

solving for `v_3`

`v_3 = 2/3 v_2= (2/3)^2 v_0 = 4` [m/s]