Solve Tension and Angles Homework: Find Smallest \theta

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SUMMARY

The discussion focuses on calculating the smallest angle θ that an archaeologist can maintain while crossing a rope between two cliffs without exceeding the rope's maximum tension of 28,000 N. The archaeologist's mass is 91.0 kg, leading to a weight of approximately 891 N. The tension formula used is Tension = (M * g) / cos(θ). The initial attempt yielded a tension of 2260 N, which was incorrect due to the omission of a factor of 2 in the calculations. A free body diagram is recommended for clarity in understanding the forces acting on the mass.

PREREQUISITES
  • Understanding of basic physics concepts, specifically tension and forces.
  • Knowledge of free body diagrams and their application in problem-solving.
  • Familiarity with trigonometric functions, particularly cosine.
  • Ability to apply Newton's second law in static equilibrium scenarios.
NEXT STEPS
  • Review the derivation of tension in static systems using free body diagrams.
  • Study the application of trigonometric identities in physics problems.
  • Learn about the implications of maximum tension limits in structural engineering.
  • Explore advanced problems involving multiple forces and angles in equilibrium.
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This discussion is beneficial for physics students, educators, and anyone interested in mechanics, particularly those studying tension in ropes and static equilibrium scenarios.

Payne0511
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Homework Statement



An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope . The rope will break if the tension in it exceeds 2.80×10^4 N, and our hero's mass is 91.0 kg.

What is the smallest value the angle \theta can have if the rope is not to break?

Homework Equations



Tension=(M*g)/cos(theta)

The Attempt at a Solution



I was able to find the tension on the rope to be 2260 N. from there I thought I could set the above equation >= to the maximum tension of the rope 28000 N and solve for theta, which gave me 1.54, but that was clearly wrong. Not too sure what else to try here..

thanks
 
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How is theta defined, with respect to the vertical or horizontal? However it is defined, draw a free body diagram. There are three forces acting on the mass, the weight and two pieces of the rope. Your expression does not have a factor of 2 in it.
 

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