a 500 kg piano is being lowered into position by a crane while two people steady

Question

a 500 kg piano is being lowered into position by a crane while two people steady it with ropes pulling to the sides. bobs rope pulls to the left, 15 degrees below horizontal, with 410 N of tension. Ellen's rope pulls toward the right, 26 degrees below horizontal.
Part A What tension must Ellen maintain in her rope to keep the piano de ending at a steady speed?
PartB What is the tension is the vertical main cable supporting the piano?
a 500 kg piano is being lowered into position by a crane while two people steady it with ropes pulling to the sides. bobs rope pulls to the left, 15 degrees below horizontal, with 410 N of tension. Ellen's rope pulls toward the right, 26 degrees below horizontal.
Part A What tension must Ellen maintain in her rope to keep the piano de ending at a steady speed?
PartB What is the tension is the vertical main cable supporting the piano?
a 500 kg piano is being lowered into position by a crane while two people steady it with ropes pulling to the sides. bobs rope pulls to the left, 15 degrees below horizontal, with 410 N of tension. Ellen's rope pulls toward the right, 26 degrees below horizontal.
Part A What tension must Ellen maintain in her rope to keep the piano de ending at a steady speed?
PartB What is the tension is the vertical main cable supporting the piano?

Explanation / Answer

Given mass of piano m = 500 kg,

   bob force Fb = 410 N, 15 degrees below horizontal left side
   Ellen force Fe =?, acting 26 degreees below horizontal , right side of the piano

a)   To keep the piano de ending at a steady speed ellen should apply the force which is equal to the Ellens' force

  
       Fb Cos 15 = Fe cos26
       Fe = Fb Cos15/Cos 26
                   = 410 Cos 15/ Cos 26
           = 440.623 N

b) now tension in the rope is T

   Here vertical forces acting on the piano are mg+Fb sin theta + Fe sin theta

       T = 500*9.8+410 sin15 + 440.623 sin 26

       T = 5199.27 N

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