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Applied PhysicsMechanics of MaterialsEngineering Mechanics

Solutions to problems related to computing the tensions in a cable given the weight and angles. It includes deriving expressions for the tensions using trigonometry and the addition formula for sine. The document also includes examples of computing the tensions for different weights and angles.

What you will learn

- Given a weight and angles, how can the tensions be computed using the derived expressions?
- What is the addition formula for the sine and how can it be used to simplify the expressions for the tensions?
- How can the tensions in a cable be expressed in terms of the weight and angles?

Typology: Summaries

2021/2022

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Download Computing Tensions in a Cable: Deriving Expressions and Solving Problems and more Summaries Physics in PDF only on Docsity! Computing the Tension in a Cable Turn to the figure below. Assume that a weight W hangs from a cable as shown. The cable is anchored firmly on the left and right. The respective angles the cable makes with the horizontal are α1 and α2 respectively. The tensions in the cable—the tension in a cable αα W T T 1 2 1 2 is the magnitude with which the cable pulls—are T1 and T2 respectively. Problem 1. Consider the weight W and the angles α1 and α2 as given and assume that the configuration depicted in the figure is stable. Draw a force diagram for the point at which the weight is suspended and use results of the section “Dealing with Forces” of Chapter 2 to express both T1 and T2 in terms of W and the angles α1 and α2. Conclude that if α1 = α2, then T1 = T2. Problem 2. Look up the addition formula for the sine and use it to simplify the expressions for T1 and T2 derived in Problem 1 to T1 = W cosα2 sin(α1 + α2) and T2 = W cosα1 sin(α1 + α2) . Problem 3. Assume that W = 500 pounds, α1 = 10◦, and α2 = 5◦ and use your the formulas of Problem 2 to compute the tensions T1 and T2. Repeat your computation of T1 and T2 with W = 1000 pounds, α1 = 5◦, and α2 = 4◦. Finally, repeat the computations once more with W = 2000 pounds and the angles α1 = 4◦ and α2 = 2◦. Problem 4. The figure below is an abstraction of Image 6. It shows a cable pulling on a utility pole with a force of magnitude T at an angle β with the horizontal. Provide an β T