A 10.0-kg picture is held in place by two wires, one hanging at 50.0° to the left of the vertical and the other at 45.0° to the right of the vertical. What is the tension in the second wire?
A) 71.8 N
B) 75.4 N
C) 98.1 N
D) 69.4 N
E) 23.8 N

Question

Quizplus · Accepted Answer

We can use the fact that the net force in the horizontal direction is zero and the net force in the vertical direction is equal to the weight of the picture (mg).

Let T1 be the tension in the left wire and T2 be the tension in the right wire. Then we have:

T1sin(50) = T2sin(45)  ... (1)

T1cos(50) + T2cos(45) = mg  ... (2)

Solving for T1 and T2 in terms of mg and substituting from (1) into (2), we get:

T2 = (mg/2)(cos(45)/sin(45) + cos(50)/sin(50))

T2 ≈ 75.4 N

Therefore, the tension in the second wire is 75.4 N (choice B).

A 100-Kg Picture Is Held in Place by Two Wires, One