Balancing act. The tightrope walker in the figure below gets tired and decides t

Question

Balancing act. The tightrope walker in the figure below gets tired and decides to stop for a rest. During this rest period, she is in translational equilibrium. She stops at middle of the rope and finds that both sides of the rope make an angle of theta = 14.10 degree with the horizontal. Sketch the walker and the rope. Show all the forces acting on the point of the rope on which the walker stands (call this point P). Also include a coordinate system (take up and to the right to be the positive directions, and the tightrope walker to be the origin). (Do this on paper. Your instructor may ask you to turn in this work.) Determine the components of all the forces on point P along the coordinate axes. (Use the following as necessary: T for the tension force and theta. Do not substitute numerical values; use variables only.) Write the conditions for static equilibrium along your two coordinate directions. (Use the following as necessary: m, g, T, and theta. Do not substitute numerical values; use variables only.) If the mass of the tightrope walker is 55 kg, what is the tension in the rope?

Explanation / Answer

the net vertical force is

2 T sin theta = mg

T = mg/ 2 sin theta

= 55 ( 9.8)/ 2 sin14.10

=1106.25 N

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