Question

Mass A (3 kg) and Mass B (1 kg) collide head‐on on a frictionless surface.  A was initially moving to the
right at 0.2 m/s, while B was moving at 0.4 m/s to the left.  The collision is completely elastic.
a) Find the velocity (magnitude and direction) for each mass after the collision.  Treat this as a one
dimensional problem.
b) Find the change in momentum for each mass.  Compare.
c) Find the change in kinetic energy for each mass.  Compare.

Answer 1

Using law of conservation of momentum

m1u1 + m2u2 = m1v1 + m2v2

3 x 0.2 - 1 x 0.4 = 3v1 + 1v2

3v1 + v2 = 0.2 ...i

Elastic collision means

v1 - v2 = u2 - u1

v1 - v2 = -0.4 - 0.2

v1 - v2 = -0.6 ... ii

solving i and ii

4v1 = -0.4

v1 = -0.1 m/s

v2 = 0.5 m/s

a)

v1 = 0.1 m/s left
v2 = 0.5 m/s right

b)

for mass 1 change in momentum = m1 (v1-u1)

= 3 ( -0.1 - 0.2)

= -0.9 kgm/s

= 0.9 kgm/s left

similarly for m2, change = 0.9 kgm/s right

c)

change in KE for 1

= 1/2 m1 (v1^2 - u1^2)

= 1.5 x (0.1^2 - 0.2^2)

= -0.045 J

similarly for 2, change

= 0.045 J

upvote if it helps