A 853 N magician (note: this is weight, not mass) is freeing himself from some shackles while suspended above a swimming pool filled with alligators.  Two ropes are suspending the magician.  The left rope makes an angle of 42 above the horizontal and points up and to the left.  The right rope makes an angle of 78 above the horizontal and points up and to the right.  Calculate the tension in the left rope, in N.

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A 853 N magician (note: this is weight, not mass) is freeing himself from some shackles while suspended above a swimming pool filled with alligators.  Two ropes are suspending the magician.  The left rope makes an angle of 42 above the horizontal and points up and to the left.  The right rope makes an angle of 78 above the horizontal and points up and to the right.  Calculate the tension in the left rope, in N.

(Please answer to the fourth decimal place - i.e 10.5432)

Expert Solution
Step 1

The expression to solve for the net force acting along the horizontal direction.

T1cosθ1=T2cosθ2T1=T2cosθ2cosθ1T1=T2cos78°cos42°T1=T20.2801

The net force acting along the vertical direction is as follows:

T1sinθ1+T2sinθ2=mg0.280T2sinθ1+T2sinθ2=mgT2=mg0.280sinθ1+sinθ22

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