Answer :
Final answer:
To calculate Young's modulus for the nylon rope used by the mountaineer, we need to know the original length, change in length, force applied, and cross-sectional area of the rope. Once we have these values, the Young's modulus (the ratio of stress to strain) can be calculated using a specific formula in terms of these given parameters.
Explanation:
The Young's modulus (E) in physics is used to measure the stiffness of an isotropic, elastic material. It is defined as the ratio of stress (force per unit area) to strain (proportional deformation) in a material. In the context of the nylon rope used by the mountaineer, we can utilize some details provided in your question to compute for E.
The original length (L) of the rope is 65m, the change in length (ΔL) is 1.2m, the force applied (F) is the weight of the climber and equals to mass times gravity (93 kg * 9.8 m/s^2), and the cross-sectional area (A) of the rope can be calculated from the diameter using πd2/4 formula.
One can use the formula for Young's modulus which is E = (F/A) / (ΔL/L). When you place all the values in the formula, you can calculate the Young's modulus in Pa. Ensure to maintain consistency in units to achieve a correct result.
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