(III) A steel cable is to support an elevator whose total...

(III) A steel cable is to support an elevator whose total
(loaded) mass is not to exceed 3100 $\mathrm{kg}$ . If the maximum
acceleration of the elevator is 1.2 $\mathrm{m} / \mathrm{s}^{2}$ , calculate the diam-
eter of cable required. Assume a safety factor of $8.0 .$

Key Concepts

Cross-sectional Area and Diameter Relationship

The cross-sectional area of a cable, which is directly linked to its diameter for circular cross-sections, determines how much load it can bear. By relating the required minimum cross-sectional area (calculated from the force to be supported divided by the material's tensile strength) to the area formula of a circle, engineers can compute the necessary diameter to safely support the load.

Material Properties and Tensile Strength

The tensile strength of a material is its maximum resistance to being pulled apart and is a critical factor in determining the load a cable can support. Understanding and using the tensile strength in conjunction with the applied safety factor allows engineers to select appropriate materials and dimensions to ensure that the cable will not fail under the expected loads.

Newton's Second Law

This law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In practical applications, it is used to determine the total force required not only to counteract gravitational force but also to provide any additional acceleration, which is crucial in designing support systems that must move or accelerate loads safely.

Safety Factor

The safety factor is a design principle used to ensure that structures or components can handle loads exceeding the expected maximum. By multiplying the calculated load by a chosen safety factor, engineers account for uncertainties in material properties, loading conditions, and potential defects, thereby improving the overall reliability and safety of the design.

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