http://www.ck12.org Chapter 7. Momentum
Illustrative Example 7.4.3
Awesome Physics Man(A)and his evil twin brother Bad Physics Man(B)each have massmand speedv. They
approach each other at right angles as shown inFigure7.16. The two collide in mortal combat and fly off together.
What is their final momentum~pimmediately after the collision? We are asked for a vector quantity and therefore
must provide both magnitude and direction.
FIGURE 7.16
Answers:
Magnitudeofmomentum
This example is a bit different than the previous ones we have encountered because it takes place in two-dimensions.
Still, the net force on the system is zero, so the total momentum of the system remains conserved.Ahas momentum
mvdirected due north andBhas momentummvdirected due west before they collide. After the collision, they must
still have the same momentum north and the same momentum west (momentum must stay conserved). We have set
up a coordinate system isFigure7.16 showing the direction of motion after the collision. The final momentum must
be composed of a northern-component of momentum ofmvnorthand a western-component of momentummvwest.
Since the components are at right angles, we can use the Pythagorean Theorem to calculate the magnitude of the
momentum. Dropping the subscripts on the velocities, we have
√
(mv)^2 +(mv)^2 =√
2 mv.Directionofmomentum
Remember that in the absence of a net force, the center of mass of a system cannot change direction or speed. This
implies that the center of mass must continue to travel along the black dashed line ofFigure7.16, both before and
after the collision. Since the components of the resultant vector are equal in magnitude, the direction of the resultant
vector must be a 45-degree angle. Using the orientation of the axes inFigure7.16, the direction of the brothers after
colliding is 90◦+ 45 ◦= 135 ◦counterclockwise as measured from the positivex−axis. We note that the orientation
of the axes are arbitrary; thex−axis could just as well have been along the direction of motion of the center of mass.
The solution could have also been found using any of the trigonometric functions.