Homework Help: Tension and Angles

1. Sep 23, 2009

Payne0511

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

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

3. 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

2. Sep 23, 2009

kuruman

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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