7.3. Conservation of Momentum and Center of Mass http://www.ck12.org
FIGURE 7.9
As seen inFigure7.9, the ball on the left is permitted to swing into the remaining hanging balls, and the ball on the
right swings out. We say the momentum of the left ball has been transferred to the momentum of the right ball. The
momentum is actually transferred through each of the balls.
The same can be demonstrated with two identical marbles. One is at rest and one is in motion, causing a head-on
collision with the marble at rest. We solve this problem (and all others, unless stated otherwise) assuming that the
interacting objects form an isolated system. InFigure7.10, marbleAhas massmand moves with velocityvialong
a horizontal surface toward marbleBwith massm, and initial velocityvBi=0. After the collision (Figure7.11),
marbleAis at rest and marbleBis moving with the final velocityvB f.
FIGURE 7.10
UsingConservation of Momentum,we first write the initial momentum of the system,piand then write the final
momentum of the systempf. Once these quantities are known, we use the conservation of momentumpi=pf.
pi=mvAi+mBi=mvAi+m( 0 ) =mvAi
pf=mvA f+mvB f=m( 0 )+mvB f
pi=pf→mvAi=mvB f→vAi=vB fWe find the final velocity of marbleBis the same as the initial velocity of marbleA. In other words, all of the
momentum of marbleAhas been transferred to marbleB. You can get a feel for the truth of this result using two
identical coins. What you’ll see when you have them collide head-on is that the first coin will stop and the second