∙Stress on a mountaineer's rope. A nylon rope used by...

$\bullet$ Stress on a mountaineer's rope. A nylon rope used by mountaineers elongates 1.10 under the weight of a 65.0 $\mathrm{kg}$ climber. If the rope is 45.0 $\mathrm{m}$ in length and 7.0 $\mathrm{mm}$ in diameter, what is Young's modulus for this nylon?

Key Concepts

Cross-sectional Area Calculation

Calculating the cross-sectional area is essential when determining stress in materials with specific geometries, such as cylindrical ropes. For a circular cross-section, the area is computed using the formula A = ?r², where r is the radius of the circle derived from the object's diameter.

Hooke's Law

Hooke's Law states that, within the elastic limit of a material, the stress applied to the material is directly proportional to the strain produced. This linear relationship is fundamental to understanding how materials respond to applied forces in their elastic region.

Young's Modulus

Young's modulus is a material property that quantifies the stiffness of an elastic material. It is defined as the ratio of stress to strain in the linear, elastic deformation region of the material, providing a measure of its resistance to being deformed when a force is applied.

Stress

Stress refers to the force exerted per unit area within a material. It is a measure of the internal forces that develop in a material in response to an external load, and is typically expressed in pascals (Pa).

Strain

Strain is a dimensionless measure of deformation representing the fractional change in length resulting from an applied stress. It is calculated as the change in length divided by the original length, indicating how much a material stretches or compresses under load.

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