A steel (Young's modulus 2.0 x 1011 N/m2) wire is strung between two supports attached to a ceiling. Initially, there is no tension in the wire when it is horizontal. A 98-N picture is then hung from the center of the wire, as the drawing illustrates, so the ends of the wire make angles of 26° with respect to the horizontal. What is the radius of the wire?

To solve this problem, we can use the concept of equilibrium. The tension in the wire will counteract the weight of the picture, so the net force on the picture is zero.

First, let's analyze the forces acting on the picture. There are two vertical forces: the weight of the picture (mg) acting downward and the tension in the wire (T) acting upward. The horizontal force is the tension in the wire.

The vertical forces can be represented as follows:
mg - T * cos(θ) = 0 (Equation 1)

The horizontal force can be represented as:
T * sin(θ) = 0 (Equation 2)

In these equations, θ represents the angle between the wire and the horizontal direction.

Since the wire is in equilibrium, the net force in both the vertical and horizontal directions is zero. We can use this information to solve for T.

From Equation 2:
T = 0

Plugging this into Equation 1:
mg - 0 * cos(θ) = 0
mg = 0

This equation tells us that the weight of the picture is zero, which is not possible. Therefore, this scenario is not physically possible, and there is no valid solution to this problem.

In conclusion, the given setup cannot be achieved with the given information.