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?

2 Answers
Mar 13, 2018

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!

Mar 13, 2018

#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]