Recently the second movie in the

*Hunger Games*triology,*The Hunger Games: Catching Fire*, was released. Many of you have probably seen it already, but I would like to preface this entry by saying that it may contain spoilers for those of you who have yet to see the movie or read the book.
I am going to talk about the scene at the end where Katniss
shoots an arrow charged with a bolt of lighting into the force field barrier to
destroy it. I would like to determine
what the tension force of the string in the bow is to allow Katniss to shoot
the arrow into the force field. In order
to preform these calculations I need to make some initial estimates and
assumptions:

__Bow:__

Mass of arrow = 0.5 kg

Change in the angle between the sting at rest and taught =
30˚

The bow doesn’t bend when the string is pulled

Katniss shoots the arrow straight up

When arrow is knocked it bisects the string

It takes 2 seconds to hit the force field

__Arena:__

Radius = 1000 m

Katniss is 50 meters from the edge of the arena when she
shoots the arrow

Given these assumptions we need to determine the distance
the arrow needs to travel:

d

^{2}=1000m^{2 }- 950m^{2}
d =312 meters

Now we can determine the average velocity of the arrow

v

_{avg }= d/t = 176 meters/2 seconds = 166 m/s
Since gravity is acting the opposite direction of the
velocity of the arrow then we know that the instantaneous velocity is equal to

166 m/s + 9.8 m/s

^{2}(1 second) = 176 m/s
Now that we know the initial velocity of the arrow, we can
determine the tension force acting on the arrow using the equation:

**Δ**KE =

**-Δ**PE

½ mv

^{2}= 2F_{T}sinθ
We want to multiply the force of tension by two because the
arrow bisects the string in two so that there are two equal tension forces
acting on the arrow. Additionally we
only are concerned with the x component of the tension force because the y
components of the two tension forces are equal but in opposite directions so
that they cancel with each other.

Therefore:

½ (0.5 kg)(176 m/s)

^{2}= 2F_{T}sin(30˚)
F

_{T }= 7744 N = 7700 N
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