Question

A 26-kg chandelier hangs from a ceiling on a vertical 4.0-m-long wire. what horizontal force would be necessary to displace its position 0.17 m to one side?

Answer 1

First of all you have that the force that is in cable in its vertical posibion is:
Fy = m * g
Fy = (26) * (9.8) = 254.8 N
Then, the force in horizontal direction will be:
Tan (x) = Fy / Fx
Clearing:
Fx = Fy / tan (x)
Substituting values:
Fx = (254.8) / (0.17 / 4)
Fx = 5995.29 N
Answer:
The horizontal force that would be necessary to displace its position 0.17 m to one side is 5995.29 N