Calculating stress, strain and Young's modulus?

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SUMMARY

The discussion focuses on calculating strain, stress, and Young's modulus for a rock climber's rope after a fall. The correct strain is calculated as 0.00153, while the stress is determined to be 11.6 MPa. The Young's modulus, initially miscalculated, is correctly found to be 7584 MPa or 7.58 GPa after proper arithmetic. The calculations for cross-sectional area and stress are confirmed as accurate.

PREREQUISITES
  • Understanding of basic physics concepts such as force, area, and material properties.
  • Familiarity with formulas for strain, stress, and Young's modulus.
  • Knowledge of unit conversions, particularly between Newtons, Pascals, and megapascals.
  • Ability to perform arithmetic calculations accurately in the context of physics problems.
NEXT STEPS
  • Study the derivation and applications of Young's modulus in material science.
  • Learn about the significance of stress-strain curves in understanding material behavior.
  • Explore the effects of different materials on Young's modulus values.
  • Investigate the implications of rope dynamics in climbing safety and equipment design.
USEFUL FOR

This discussion is beneficial for physics students, material scientists, and rock climbing safety professionals who seek to understand the mechanical properties of climbing ropes and their implications in real-world scenarios.

rockchalk1312
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After a fall, a 77 kg rock climber finds himself dangling from the end of a rope that had been 15 m long and 9.1 mm in diameter but has stretched by 2.3 cm. For the rope, calculate (a) the strain, (b) the stress, and (c) the Young's modulus.


strain = ΔL/L
stress = F/A
Young's modulus = (F/A)/(ΔL/L)


I haven't gotten any of these right and I have no idea what I'm doing wrong on them.

a) 2.3 cm = .023 m / 15 m = .0015

b) A = ∏r2 = (∏)(.0091/2)2 = 6.503E-5 m2
stress = ((77)(9.8))/(6.503E-5) = 1.16E7 N/m2

c) (754.6/6.503E-5) / (.023/15) = .756

None of those were right; also I thought Young's modulus was supposed to be a huge number so obviously that's not right. Any help is appreciated!
 
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The strain was correct, although they may have given the result with more digets 0.00153.

The calculation of the cross sectional area is correct.

The calculated stress is correct, but perhaps should be expressed as 11.6 MPa.

The calculated Young's modulus, which is the stress divided by the strain is incorrect. You made a mistake in arithmetic. 11.6/0.00153 = 7584 MPa = 7.58 GPa.
 
All of those helped me! The computer just wanted them entered in an odd way. Thank you!
 

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