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.
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
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?