(II) (a) What is the minimum cross-sectional area required...

Name: Problem 53, Chapter 9: Physics: Principles with Applications
Uploaded: 2023-12-04T15:45:07-08:00
Duration: 4 min 18 s
Channel: Prabhat Tyagi
Description: (II) (a) What is the minimum cross-sectional area required of a vertical steel cable from which is suspended a 270-kg chandelier? Assume a safety factor of 7.0. (b) If the cable is 7.5 m long, how much does it elongate?

(II) (a) What is the minimum cross-sectional area required of a vertical steel cable from which is suspended a 270-kg chandelier? Assume a safety factor of 7.0. (b) If the cable is 7.5 m long, how much does it elongate?

Key Concepts

Tensile Stress

Tensile stress is the internal resistance that a material exhibits when a force is applied axially, causing it to be stretched. It is calculated by dividing the applied force by the cross-sectional area of the material. Understanding tensile stress is essential in determining a cable's ability to support a load without failing, as the material must withstand the stress imposed by the suspended weight.

Safety Factor

A safety factor is a design parameter used to provide a margin of error in engineering calculations. It involves increasing the required strength of a material beyond the expected load to account for uncertainties such as material imperfections, unexpected loads, or variations in manufacturing. This approach ensures that even under adverse conditions, the structure will perform safely.

Young's Modulus and Elastic Deformation

Young's modulus is a measure of a material’s stiffness and is defined as the ratio of stress to strain in the elastic region of the material's deformation. It plays a critical role in predicting how much a material will elongate under a given load. By applying Hooke's Law, the elongation of a material (within the elastic limit) can be calculated using the formula ? = (F·L)/(A·E), linking the applied force, the original length, the cross-sectional area, and Young's modulus.

Determination of Cross-Sectional Area

Determining the cross-sectional area required for a load-bearing member involves ensuring that the tensile stress generated by the applied load, when divided by the area, remains below the allowable stress. The allowable stress is typically obtained by taking the material's yield strength and dividing it by the safety factor. This calculation is critical in designing structures and components that will not fail under the expected loads.

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