500kg Piano is lowered by a crane and steadied by tow ropes; Bob\'s rope is at 1

Question

500kg Piano is lowered by a crane and steadied by tow ropes; Bob's rope is at 15 degrees below the x-axis with a 500N of tension and Ellen's Rope at 25 degrees below the horizontal. A. What is the tension of Ellens rope needed to keep the piano descending vertically? B. What is the tension on the cable from the crane? 500kg Piano is lowered by a crane and steadied by tow ropes; Bob's rope is at 15 degrees below the x-axis with a 500N of tension and Ellen's Rope at 25 degrees below the horizontal. A. What is the tension of Ellens rope needed to keep the piano descending vertically? B. What is the tension on the cable from the crane?

Explanation / Answer

The mass of the piano m = 500kg the tension in the Bob's rope TB = 500N a) To keep the piano from veering to one side or the other, Ellen's horizontal force must cancel Bob's. Thus: TE * cos(25 deg) = 500*cos(15 deg) TE = 500*(cos15 /cos25) = 500*(0.9659/0.90631) = 532.89 N or 533 N b) The tension in the rope must balance the force of gravity and the force of the two pullers: T = 500*9.8 + 500*sin15 + 533*sin25 = 5254.66N

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