Simple Nature - Light and Matter

ae/Discussion question A.

af/Discussion question E.

this to thexcomponent of the acceleration, we find

x=

∫ (∫

axdt

)

dt

=

∫

(axt+vxo)dt,

wherevxois a constant of integration, and

x=

1

2

axt^2 +vxot+xo.

Similarly,y=(1/2)ayt^2 +vyot+yoandz= (1/2)azt^2 +vzot+zo. Once

one has gained a little confidence, it becomes natural to do the

whole thing as a single vector integral,

r=

∫ (∫

adt

)

dt

=

∫

(at+vo)dt

=

1

2

at^2 +vot+ro,

where now the constants of integration are vectors.

Discussion Questions

A In the game of crack the whip, a line of people stand holding hands,
and then they start sweeping out a circle. One person is at the center,
and rotates without changing location. At the opposite end is the person
who is running the fastest, in a wide circle. In this game, someone always
ends up losing their grip and flying off. Suppose the person on the end
loses her grip. What path does she follow as she goes flying off? Draw an
overhead view. (Assume she is going so fast that she is really just trying
to put one foot in front of the other fast enough to keep from falling; she
is not able to get any significant horizontal force between her feet and the
ground.)

B Suppose the person on the outside is still holding on, but feels that
she may loose her grip at any moment. What force or forces are acting
on her, and in what directions are they? (We are not interested in the
vertical forces, which are the earth’s gravitational force pulling down, and
the ground’s normal force pushing up.) Make a table in the format shown
in subsection 3.2.6.

C Suppose the person on the outside is still holding on, but feels that
she may loose her grip at any moment. What is wrong with the following
analysis of the situation? “The person whose hand she’s holding exerts
an inward force on her, and because of Newton’s third law, there’s an
equal and opposite force acting outward. That outward force is the one
she feels throwing her outward, and the outward force is what might make
her go flying off, if it’s strong enough.”

D If the only force felt by the person on the outside is an inward force,
why doesn’t she go straight in?

Section 3.4 Motion in three dimensions 215