Static equilibrium: A 7 kg sign is hung up with two cables, with each cable at a 40-degree angle. What is the force in the cables?
Once again, we are going to solve this problem by balancing the forces
in the y-direction. What can we figure out right away? The force of gravity on
the sign in the downwards direction.
Fg = m ∗ g
Fg = 7kg ∗ 10m/s2 = 70N
The forces acting upward on the sign have to cancel out this 70N downward
force. These upward forces are the y components of each of the diagonal forces.
Because we know the two diagonal forces are equal (the angles are the same),
we know that they split the weight equally. Therefore, the y component of
each must be 35 (35 up + 35 up balances 70 down ). Then, once again, we do
sohcahtoa. The y component is the side opposite to the angle:
sin40 = 35/F
Where F is the diagonal force we are looking for.
F = 35/sin40 = 54.45N