Simple Nature - Light and Matter

h/Example 56.

of the three components,

∆px= 0

∆py= 0

∆pz= 0,

or as a single vector equation,^16

∆p= 0.

The following table summarizes some vector operations.

operation definition

|vector|

√

vector^2 x+vector^2 y+vector^2 z

vector+vector Add component by component.

vector−vector Subtract component by component.

vector · scalar Multiply each component by the scalar.

vector/ scalar Divide each component by the scalar.

The first of these is called themagnitudeof the vector; in one dimen-

sion, where a vector only has one component, it amounts to taking

the absolute value, hence the similar notation.

self-check J

Translate the equationsFx=max,Fy=may, andFz=mazinto a single

equation in vector notation. .Answer, p. 1056

An explosion example 56

.Astronomers observe the planet Mars as the Martians fight a

nuclear war. The Martian bombs are so powerful that they rip the

planet into three separate pieces of liquefied rock, all having the

same mass. If one fragment flies off with velocity components

v 1 x = 0,v 1 y=1.0x10^4 km/hr, and the second withv 2 x=1.0x10^4

km/hr,v 2 y= 0, what is the magnitude of the third one’s velocity?

.We work the problem in the center of mass frame, in which

the planet initially had zero momentum. After the explosion, the

vector sum of the momenta must still be zero. Vector addition can

be done by adding components, so

mv 1 x+mv 2 x+mv 3 x= 0

and

mv 1 y+mv 2 y+mv 3 y= 0,

where we have used the same symbolmfor all the terms, be-

cause the fragments all have the same mass. The masses can

(^16) The zero here is really a zerovector, i.e., a vector whose components are
all zero, so we should really represent it with a boldface 0. There’s usually not
much danger of confusion, however, so most books, including this one, don’t use
boldface for the zero vector.
198 Chapter 3 Conservation of Momentum