Ball A is moving at 5.5 m/s in the positive direction and collides head on with

Question

Ball A is moving at 5.5 m/s in the positive direction and collides head on with ball B traveling at 4.0 m/s from the opposite (negative) direction of ball A. If ball A has a mass of 4.5kg and ball B has a mass of 2.8kg, find the final velocity of each mass for each of the following situations.

a.) The bodies stick together
(4.5kg mass)?
(2.8kg mass)?

b.) Collision is Elastic
(4.5kg mass)?
(2.8kg mass)?

c.) The 2.8kg body is at rest after the collision
(4.5kg mass)?
(2.8kg mass)?

d.)The 4.5kg body has a velocity of 4.0m/s in the negative direction after the collision.
(4.5kg mass)?
(2.8kg mass)?

Explanation / Answer

a) If bodies stick together they move with the same velocity

from conservation of momentum before and after collision
m1u1+m2u2=(m1+m2)v (here ,m1 ,m2 are masses of two balls ,u1 ,u2 are initial velocities and v is final velocity of combined mass)

velocity,v = (4.5*5.5-2.8*4.0) /(4.5+2.8) = +1.7 m/s (- sign is for the ball moving in opposite direction)

two balls move at 1.7 m/s velocity

b) for the collision elastic ,both the momentum and K.E are conserved ,

so    m1u1+m2u2=m1v1+m2v2 , m1u12+m2u22=m1v12+m2v22

from this , u1-u2 = v2- v1

v1 = ((m1-m2)u1 + 2m2u2)/(m1+m2) ,v2 = (2m1u1 + (m2-m1)u2)/(m1+m2)

so ,v1= -1.79 m/s ,v2 =+7.71 m/s

c) 2.8 kg body mass is at rest after collision , so v2 =0

v1=m1u1+m2u2/m1

v1 = +3.01 m/s and v2 =0

d) 4.5 kg mass is moving at -4.0 m/s velocity then

   v2= (m1(u1- v1)+m2u2)/m2

v2 = +11.27 m/s and v1= -4.0 m/s

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