Solve Tension and Angles Homework: Find Smallest \theta

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The discussion centers on calculating the smallest angle \(\theta\) that an archaeologist can maintain while crossing a rope without exceeding its tension limit of 28,000 N. The initial calculation of tension yielded 2,260 N, which was deemed incorrect when attempting to solve for \(\theta\). Participants suggest using a free body diagram to analyze the forces acting on the mass, including weight and rope tension. It is noted that the tension equation must account for two segments of the rope, indicating that a factor of 2 is necessary in the calculations. The conversation emphasizes the importance of correctly defining \(\theta\) and accurately applying the tension formula to find the solution.
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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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