Centripetal Force

[victorias]

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A 20kg child sits on a swing with ropes 2 m long. The maximum speed during each swing is 4 m/s with an arc of 135°. What is the maximum tension in the swing?

The answer states that Fc + Fg = T but isn't T and Fc both pointing to the centre? So shouldn't it be Fc + T = Fg? I am having difficulty in set up for this problem.

 

[Lawpy]

The centripetal force is the same as the net force in circular motion. You are correct that Fc and T are in the same direction pointing towards the top of the swing. However, because the swing is occurring at various angles, we are dealing with components of the gravitational force (because Fg is always pointing down).

The motion of the swing can be described by drawing a free-body diagram like below

So: Fc = T - mgcos(theta) or T = Fc + mgcos(theta). Maximum tension occurs when theta = 0.