This question involves finding the velocity of the center of mass of colliding objects that stick together.

Question

Consider the head-on collision of two masses,
m1 = m, with initial velocity v1 = v0, and
m2 = 2m with its initial velocity v2 =v0/2
.
After the collision they stuck together.
Find the velocity of the center of mass, vCM

 

Possible Answers:

 

1. −v0/2
2. 0
3. v0
4. v0/2
5. −v0

Answer 1

Use conservation of linear momentum.  Assuming m₁ initially moves in the positive direction and m₂ moves in the opposite direction,

 

m₁v₁ - m₂v₂ = (m₁ + m₂)v

 

mv₀ - (2m)(v₀/2) = (m + 2m)v

 

0 = 3v

 

v = 0

 

The center of mass does not move in this problem.