6 An object of mass M moving at V m/s collides with a stationary object of mass

Question

6 An object of mass M moving at V m/s collides with a stationary object of mass 2M. The collision is elastic. After collision the object of mass M has a final speed of v1 and the object of mass 2M has a final speed of mass v2 (a) Show that the relationship between the final velocities v1 and v2 is (4 marks) 2v1 = -v2 (b) Show that for the final velocities are related to the initial velocity V by (4 marks) (c) Calculate the final velocities of the elastic collision between a moving object of mass of 1.0 kg and an initial velocity of 3.0 m/s with a stationary object of mass 2.0 kg (2 marks)

Explanation / Answer

Here , using conservation of momentum

M * v1 + 2 M * v2 = m V

v1 + 2 v2 = V ----(1)

and as the collision is elastic ,

coefficient of resitition is 1

1 = (v2 - v1)/V

V = v2 - v1 ----(2)

from 1 and 2 ,

v1 + 2 v2 = v2 - v1

v2 = -2 v1

hence , proved

b)

putting v2 = -2 v1 in 1 ,

v1 -4 v1 = V

v1 = -V/3

and v2 = -2v1

v2 = 2V/3

hence ,

v1 = -V/3 , v2 = 2V/3

c)

Here , in this case ,

V = 3 m/s

v(1 kg ) = -V/3

v(1 kg ) = -1 m/s

v(2 kg) = 2V/3

v(2 kg) = 2 m/s

the velocity of 1 Kg is -1 m/s

velocity of 2 Kg is 2 m/s

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