Momentum in an isolated system, where no net external forces act, is always conserved. A rough
approximation of a closed system is a billiard table covered with hard tile instead of felt. When the
billiard balls collide, they transfer momentum to one another, but the total momentum of all the balls
remains constant.
The key to solving conservation of momentum problems is remembering that momentum is a vector
.
A satellite floating through space collides with a small UFO. Before the collision, the satellite was
traveling at 10 m/s to the right, and the UFO was traveling at 5 m/s to the left. If the satellite’s mass is
70 kg, and the UFO’s mass is 50 kg, and assuming that the satellite and the UFO bounce off each other
upon impact, what is the satellite’s final velocity if the UFO has a final velocity of 3 m/s to the right?Let’s begin by drawing a picture.
Momentum is conserved, so we write
The tick marks on the right side of the equation mean “after the collision.” We know the momentum of
each space traveler before the collision, and we know the UFO’s final momentum. So we solve for the
satellite’s final velocity. (Note that we must define a positive direction; because the UFO is moving to the
left, its velocity is plugged in as negative.)
Now, what if the satellite and the UFO had stuck together upon colliding? We can solve for their final
velocity easily: