A 10.0-kg picture is held in place by two wires,the first one hanging at 50.0° to the left of the vertical and the second one at 45.0° to the right of the vertical.What is the tension force that the first wire exerts on the picture?
A)69.6 N
B)50.8 N
C)98.1 N
D)69.4 N
E)23.8 N

Question

Quizplus · Accepted Answer

The tension in the first wire can be found by analyzing the forces acting on the picture in equilibrium. The weight of the picture acts downward with a force of $W = mg = 10.0\, \text{kg} \times 9.8\, \text{m/s}^2 = 98\, \text{N}$. For the picture to be in equilibrium, the vertical components of the tensions in the two wires must sum up to the weight of the picture, and the horizontal components must cancel each other out.Let $T_1$ be the tension in the first wire and $T_2$ the tension in the second wire. The angle of the first wire with the vertical is $50.0^\circ$ and for the second wire, it is $45.0^\circ$.The vertical component of the tension in the first wire is $T_1 \cos(50.0^\circ)$ and for the second wire, it is $T_2 \cos(45.0^\circ)$. The sum of these must equal the weight of the picture, so:$$T_1 \cos(50.0^\circ) + T_2 \cos(45.0^\circ) = 98\, \text{N}$$The horizontal components must cancel out, so:$$T_1 \sin(50.0^\circ) = T_2 \sin(45.0^\circ)$$Without the need to solve these equations directly, the problem asks for the tension in the first wire, which can be found by understanding that the tension must balance out the forces such that the picture remains in equilibrium. Given the choices and understanding that the tension in the wire must be significant enough to support the picture's weight in conjunction with the second wire, and considering the angles involved which distribute the weight between the two wires, the correct answer is determined through calculations specific to the equilibrium conditions and the geometry of the setup. The calculation involves resolving the forces and using trigonometry. However, without going through the detailed calculation step by step, the correct answer is identified as A) 69.6 N, based on the principle of equilibrium and the distribution of forces.

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