a horizontal wire is stretched between two vertical poles. when a 12.0-N weight is suspended at its center, the wire sags until the angle between its halves is 110 degrees. what are the forces exerted by each half of the wire in supporting the weight?

Question

a horizontal wire is stretched between two vertical poles. when a 12.0-N weight is suspended at its center, the wire sags until the angle between its halves is 110 degrees. what are the forces exerted by each half of the wire in supporting the weight?

i don't really get the question..and how to solve it

Each half of the wire applies a tension force T at an angle of (180-110)/2 = 35 degrees to the horizontal. The sum of the vertical components of these forces equals the weight (12 N).

Thus 2 T sin 35 = 12 N
Solve for the tension force t.

Answer 1

To solve this problem, we can use the concept of equilibrium. In this case, when the weight is suspended at the center of the wire, the wire sags until the angle between its halves is 110 degrees.

First, let's consider the forces acting on the left half of the wire. We can break down the force into its horizontal and vertical components. The tension force (T) exerted by the left half of the wire can be divided into two components: one parallel to the horizontal direction and the other perpendicular to the vertical direction.

Since the wire is in equilibrium, the vertical components of the forces exerted by the left and right halves of the wire should add up to balance the weight. The weight is given as 12.0 N. Thus, the vertical component of the force exerted by each half of the wire will be equal to 12.0 N divided by 2, which is 6.0 N.

Using trigonometry, we can determine the tension force T. We know that the angle between the halves of the wire is 110 degrees. Since each half of the wire forms an angle of 110/2 = 55 degrees with the horizontal, we can find the horizontal component of the tension force by using the cosine function.

Cosine (55) = Adjacent / Hypotenuse

Cosine (55) = T (horizontal component) / T (total tension force)

To find T (horizontal component), rearrange the equation:

T (horizontal component) = Cosine (55) * T (total tension force)

Similarly, the vertical component of the tension force can be found using the sine function:

Sine (55) = Opposite / Hypotenuse

Sine (55) = T (vertical component) / T (total tension force)

To find T (vertical component), rearrange the equation:

T (vertical component) = Sine (55) * T (total tension force)

Now we have equations for the horizontal and vertical components of the tension force. To solve for T, we can use the fact that the sum of the vertical components of the forces exerted by the left and right halves of the wire equals the weight (6.0 N):

T (vertical component) + T (vertical component) = 6.0 N

Substituting the values we obtained earlier:

Sine (55) * T (total tension force) + Sine (55) * T (total tension force) = 6.0 N

2 * Sine (55) * T (total tension force) = 6.0 N

Divide both sides by 2 * Sine (55):

T (total tension force) = 6.0 N / (2 * Sine (55))

Now that we have the value for T (total tension force), we can plug it back into the equations for the horizontal and vertical components to find the individual tension forces exerted by each half of the wire.