Tension in a Pendulum? why does mgcos(theta) not effect it?

[ipodtouch]

The BR notes the pendulum equation for T

T= mgsin(theta) + Fc

I was wondering why the outward force mgcos(theta) is not in this equation. It seems confusing to me why we include the Perpendicular force when there is a much stronger 180 degree opposing force.

I was also wondering, is mgcos(theta) equal to the CENTRIFUGAL force?
If it doesn't affect the tension, what is centrifugal force's relationship to this whole party?

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[SaintJude]

It does, the equation is incorrect. mgsin (theta) is the restoring force and acts perpendicular to the tension.

The equation for tension in a swing pendulum is

T = mgcos θ + mv^2/r

Someone asked a similar question earlier, so I'll back my post up with some rationale:

Newton's law is net force = ma so

draw the forces in the direction along the tension of the pendulum and you'll see that T = y-component of the weight, so
ΣFy = mac → T - mg cos θ = mac

So T= mac + mg cos θ = mv^2/r + mg cos θ

 

[ipodtouch]

oh man that makes so much more sense. I must have written the equation down wrong.

 

[milski]

Keep in mind that it may be sin or cos, depending on what exactly is θ - it could be the angle with the equilibrium position or it could be the angle with the horizontal.

 

[SaintJude]

Ah yes! That's a really good point.