By Sophi Lederer (September 25, 2016)

The other day at soccer training,
as I was going through the motions of a drill, I was struck by the physics that
was involved. In the drill, each player got a partner and a ball. The two
players started with one foot on top of the ball, and when the coach said “go”,
each player pulled backwards on the ball and tried to win it. (Set-up shown
above.) What I realized was that this drill involved competing forces acting on
an object – the ball. I also realized that the applied force with the greatest magnitude
in the x-direction would ultimately win the ball.

In the
picture above, my foot will be the addidas cleat, and my partner’s foot will be
the nike cleat. The yellow arrows indicate the force applied to the ball by
myself and my partner. The red lines indicate the x and y components of each
force. We will assume that my partner and I have equal strength and therefore
our overall applied forces will have equal magnitudes. However, our forces
differ in the angle at which they are applied. Thus, the force that will win
the ball will be the one with the greatest x-component. To maximize my force’s
x-component, I tried to angle my force such that it was more parallel to the
ground. Here is how it works (using arbitrary values for force):

__Me (Addidas cleat)__

__Partner (Nike cleat)__

F(applied) = 100 N F(applied)
= 100 N

q = 20° below the x-axis q
= 45° below the x-axis

x-component of F(applied): x-component
of F(applied):

cos(20°) = x/100 cos(45°)
= x/100

**x = 94 N**

**x = 71 N**

Thus, by reducing the angle of my applied force below the
x-axis (making my force more parallel to the ground), I was able to increase the
x-component. On the other hand, my partner applied her force at a greater angle
downwards, so her force in the x-direction was less. As a result, my force’s
x-component overcame that of my partner, and I was able to pull the ball
backwards and win the game.

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