Chapter 2, Problem 38A

Sneezlee’s wire supports are repositioned as shown. How does the tension in each wire compare with the tension of the previous question?

To determine

To Compare: The tension in each wire with the weight of the bird.

Explanation of Solution

Introduction:

In previous question, the wires were nearly vertical due to which in each wire, the tension was greater than the half of the weight of the bird.

The formula of tension calculated from the previous problem:

  $T=\frac{1}{2\sin \theta }W$

Where,

  $W=$ Weight of the bird.

  $T=$ Tension in the rope.

  $\theta =$ Angle of each rope with the horizontal.

According to the formula, if the angle of each rope with the horizontal is $30°$ , the tension in each rope would be equal to the weight of the bird. If angle exceeds $30°$ , the tension of each wire would exceed the weight of the bird.

Conclusion:

Hence, the tension in each wire would be equal to the weight of the bird, if angle of the rope is equal to $30°$ . Further increasing the angle, the tension would exceed the weight of the bird.