Mountain climber - center of gravity, tension, angles

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SUMMARY

The discussion centers on a physics problem involving a mountain climber rappelling down a vertical wall. The climber, weighing 770 N, has a rope attached 15 cm to the right of his center of gravity. The correct solutions identified are a tension in the rope of 750 N and a contact force of 310 N exerted by the wall at an angle of 22° above the horizontal. The problem emphasizes the application of equilibrium conditions, where the sum of forces and torques must equal zero.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of trigonometric functions (sine, cosine, tangent)
  • Familiarity with equilibrium conditions in physics
  • Basic problem-solving skills in statics
NEXT STEPS
  • Study the principles of static equilibrium in physics
  • Learn how to apply trigonometric functions to solve force problems
  • Explore examples of tension and contact forces in real-world applications
  • Review advanced problems involving multiple forces and torques
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the mechanics of forces in equilibrium scenarios, particularly in climbing and outdoor activities.

BlueSkyy
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Homework Statement



A mountain climber is rappelling down a vertical wall (the figure below ). The rope attaches to a buckle strapped to the climber's waist 15 cm to the right of his center of gravity. If the climber weighs 770 N, find (a) the tension in the rope and (b) the magnitude and direction of the contact force exerted by the wall on the climber's feet.

https://chip.physics.purdue.edu/protected/GiambattistaMimg/chapter-08/fig-064.gif

# (a) 750 N; (b) 310 N at 22° above the horizontal
# (a) 730 N; (b) 330 N at 19° above the horizontal
# (a) 730 N; (b) 300 N at 16° above the horizontal
# (a) 750 N; (b) 330 N at 19° above the horizontal
# (a) 770 N; (b) 300 N at 16° above the horizontal

Homework Equations



basic equations...
F = ma
sin = o/h
cos = a/h
tan = o/a

The Attempt at a Solution



well...
i don't really know where to start.
i have examples of the rope being attached to the climber's CoG, so i tried to work the problem like one of those and came out with a tension of 744 N.

any help would be GREATLY appreciated!
 
Physics news on Phys.org
This is an equilibrium problem, so apply the conditions for equilibrium: The forces (in any direction) must add to zero and the torques (about any point) must add to zero.
 

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