An Alternate Solution Using Conservation of Momentum

Example 2: Finding the Velocity After an Inelastic Collision - Both Objects Initially Moving

Having both colliding objects moving before the collision introduces no major complications (just one additional term to deal with) to the solution, as shown below.

Two meatballs are speeding directly toward each other. One is a 4.0-kg meatball moving with a speed of 6.0 m/s, and the other has a mass of 2.0 kg and a speed of 4 m/s. If they collide inelastically, what will be the speed of the resulting 6.0 kg meatball immediately after the collision?


problem diagram

Since no external forces act on the two-meatball system (it is an "isolated system"), the total momentum of the system is conserved. The momentum before the collision is:

pbefore = m1v1 + m2v2

and the total system momentum after the collision is:

pafter = (m1 + m2)v

"Momentum is conserved" means:

pafter = pbefore

so that:

(m1 + m2)v = m1v1 + m2v2


The 6.0-kg meatball has a velocity of about 2.7 m/s immediately after the collision.

last update April 4, 2006 by JL Stanbrough