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. Bob's rope pulls to the left, 15 degrees below horizontal, with 500 N of tension. Ellyn's rope pulls toward the right, 25 degrees below the horizontal.

What tension must Ellyn maintain in her rope to keep the piano descending vertically? The answer is 532.89 N.

Now for the part I can't answer: What tension must the vertical main cable provide to ensure that the piano descends vertically at constant speed?

Explanation / Answer

draw a diagram to get a visual of the relationships between the forces the x components (horizontal) of the two guide ropes must be equal Fx = 500 cos15 = Ft cos25 solve for Ft --- tension in Ellen's rope the tension in the lift cable is equal to the weight of the piano plus the downward, y, components of the guide ropes Fc = 500*9.81 + 500 sin15 + Ft sin25

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