Question

Two particles, ?1 and ?2, undergo a glancing elastic collision. Initially mass ?1 moves along the negative ?-direction and ?2 along the positive ?-direction, both with speed ?? . After the collision ?1 moves along the negative ?-direction. Given that ?2 = 8 ?1, find the magnitudes of the velocities of both particles in terms of ?? , and the direction of mass ?2.

Answer 1

In y direction, conservation of momentum

-m1ui + m2ui = m2 v2y

m2 = 8 m1

-m1ui + 8m1ui1 = 8m1 v2y

v2y = 7ui/8 in +y direction

in x direction, conservation of momentum,

0 = -m1v1 + m2v2x

v1 = 8v2x

conservation of kinetic energy

1/2 m1 ui^2 + 1/2 8 m1 ui^2 = 1/2 m1 v1^2 + 1/2 8m1 v2^2

9ui^2 = v1^2 + 8v2^2

9ui^2 = 64 v2x^2 + 8(v2x^2 + v2y^2)

9ui^2 = 72 v2x^2 + 49/8 ui^2

v2x = 0.1998 ui

Magnitude of velocity of m2 = 0.8975 ui

magnitude of velocity of m1 = 1.5986 ui

direction of m2 = 77 degrees from + x axis (CCW)