One end of a uniform wire of length L and of weight W is...

One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof and a weight $W_{1}$ is suspended from its lower end. If $S$ is the area of cross-section of the wire, the stress in the wire at height ( $3 L / 4$ ) from its lower end is

Key Concepts

Tensile Stress

Tensile stress refers to the force per unit area acting along the cross-section of a material when it is subjected to a pulling or stretching load. It is calculated by dividing the force that a material experiences by its cross?sectional area. This concept is fundamental when analyzing how materials behave under loads to ensure they remain within safe operational limits.

Free-Body Diagram Analysis

A free-body diagram is a graphical tool used to isolate and represent all the forces acting on a specific part of a structure or system. In the context of analyzing a wire under load, it helps in determining the net force at any section by accounting for both external loads (like a suspended weight) and internal forces due to the distributed weight of the wire itself.

Uniform Weight Distribution

Uniform weight distribution pertains to the characteristic of a material or structural element where its weight is evenly spread along its length. For a uniform wire, this means that any segment of the wire carries a weight proportional to its length. This concept is essential for calculating the portion of the wire’s total weight acting at a particular point along the wire.

Force Equilibrium

Force equilibrium is a core principle in mechanics which states that, for a body or system in static balance, the sum of all forces acting on it must equal zero. This principle is used to analyze sections of the wire to determine the resultant tension created by both the attached mass and the weight of the portion of the wire below the point of interest.

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