A 5,500-N weight is suspended in equilibrium by two cables.Cable 1 applies a horizontal force to the right of the object and has a tension,T₁.Cable 2 applies a force upward and to the left at an angle of 38.0° to the negative x-axis and has a tension,T₂.Find T_2. A) 7,040 N B) 3,390 N C) 8,930 N D) 6,980 N E) 4,330 N

Question

Quizplus · Accepted Answer

We can start by drawing a free-body diagram of the weight and the two cables: ``` ^ T2 | T1 <---| | weight | v ``` Using trigonometry, we can find the horizontal and vertical components of T2: ``` ^ T2 * sin(38°) = T2y | T1 <---| | weight | v T2 * cos(38°) = T2x ``` Since the weight is in equilibrium, the forces in the x and y directions must balance: ``` ƩFx = T1 - T2x = 0 => T1 = T2x ƩFy = T2y - weight = 0 => T2y = weight = 5500 N ``` Substituting T2x and T2y in the equation for T1, we get: ``` T1 = T2 * cos(38°) = 5500 N / sin(38°) * cos(38°) = 8930 N ``` Therefore, the correct answer is C) 8,930 N.

A 5,500-N Weight Is Suspended in Equilibrium by Two Cables