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 ? = 11.00

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 ? = 11.00° with the horizontal. (b) 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 ?. Do not substitute numerical values; use variables only.) (c) Write the conditions for static equilibrium along your two coordinate directions. (Use the following as necessary: m, g, T, and ?. Do not substitute numerical values; use variables only.) Fx = _______ = 0 Fy =_______ = 0 (d) If the mass of the tightrope walker is 60 kg, what is the tension in the rope? T = _______ N

Explanation / Answer

1)

Both sides of the rope makes same angle with the horizontal. so,

T_xR = T cos 11

T _yR = T sin 11

T_ xL = - T cos 11

T_yL = T sin 11

c)

F x = 0

Fy = 2 T sin 11 - mg = 0

d)

2 T sin 11 = m g

T = mg / 2 sin 11

= ( 60 kg ) ( 9.8 m/s^2) / 2 sin 11

=1540.8 N

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