What is the tension in the cord holding a suspended sphere at a 23° angle?

[farleyknight]

Homework Statement

A sphere of mass 1.1 × 10^-4 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes a constant angle of 23° with the vertical. Find (a) the magnitude of that push and (b) the tension in the cord.

Homework Equations

F_g = m*g

F_net = 0 (since we are in equilibrium)

The Attempt at a Solution

I am attempting (b) first, then (a) should follow naturally

Firstly, since the sphere is not moving, we have

F_net,y = 0

So then we can take the sum of the two forces acting along the vertical to get

F_g,y + T_y = 0

Where T_y is the vertical component of the tension in the cord. Taking the projection to the y coordinate, and expanding the definition of gravity, we have

-mg + T*sin(t) = 0

or

T = (mg) / sin(t) = (1.1*10^-4)*(9.8) / sin(23) == 27.58 * 10^-4 N

But this solution isn't working for me.. Any idea where I went wrong?

 

[rl.bhat]

T * cos23 = mg.

 

[farleyknight]

T * cos23 = mg.

SOH-CAH-TOA, duh...

Thank you, sir