Two artifacts in a museum display are hung from vertical walls by very light wires, as shown in the figure.Find the tension in the horizontal wire ifw=158Nandm=30.0 kg.

To find the tension in the horizontal wire, we need to consider the forces acting on the artifact.

First, let's label the variables:
- T1 = tension in the horizontal wire
- T2 = tension in the diagonal wire
- w = weight of the artifact
- m = mass of the artifact

Since both artifacts are hung from very light wires, we can ignore the weight of the wires themselves.

Now, let's analyze the forces acting on the artifact:
1. Weight (w): The weight of the artifact acts vertically downward and can be calculated using the formula w = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).

2. Tension in the vertical wire (T2): The tension in the diagonal wire also acts vertically and helps counterbalance the weight. Since the forces are in equilibrium, T2 = w.

3. Tension in the horizontal wire (T1): The tension in the horizontal wire is responsible for maintaining the horizontal equilibrium of the artifact. It acts as a balancing force against the horizontal component of the weight.

Now, let's find T1:
To find the horizontal component of the weight, we can use the equation w_h = w * sin(theta), where theta is the angle between the vertical and horizontal wires.

Since the weight is vertically downward, sin(theta) will be equal to the opposite side length (m) divided by the hypotenuse (w):
sin(theta) = m / w

Therefore, the horizontal component of the weight becomes:
w_h = w * sin(theta) = w * (m / w) = m

Since T1 balances the horizontal component of the weight, we have:
T1 = w_h = m

Therefore, the tension in the horizontal wire is equal to the mass of the artifact, which is 30.0 kg in this case.