After a fall, a 95 kg rock climber finds himself dangling...

After a fall, a 95 kg rock climber finds himself dangling from the end of a rope that had been 15 $\mathrm{m}$ long and 9.6 $\mathrm{mm}$ in diameter
but has stretched by 2.8 $\mathrm{cm} .$ For the rope, calculate (a) the strain,
(b) the stress, and (c) the Young's modulus.

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Key Concepts

Young's Modulus

Young's Modulus, or the modulus of elasticity, is the ratio of stress to strain in a material within its elastic limit. It characterizes the stiffness of a material; a higher Young’s modulus indicates that the material is less prone to deformation under stress. This concept is essential in determining how elastic a material is in response to applied forces.

Stress

Stress is defined as the force applied per unit area within materials. It quantifies the internal forces that neighboring particles of a continuous material exert on each other. Stress is measured in pascals (Pa) and is a key factor in determining whether a material will deform or fail under a load.

Strain

Strain is the measure of deformation representing the fractional change in length of a material when a force is applied. It is calculated as the change in length divided by the original length and is a dimensionless quantity. This concept is fundamental in understanding how materials elongate or compress under load.

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