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° below horizontal, with 500 N of tension. Ellen's rope pulls toward the right, 25° below horizontal. What tension must Ellen maintain in her rope to keep the piano descending vertically at constant speed? What is the tension in the vertical main cable supporting the piano?

Question

Physics

Whiskers

6 April, 10:37

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° below horizontal, with 500 N of tension. Ellen's rope pulls toward the right, 25° below horizontal. What tension must Ellen maintain in her rope to keep the piano descending vertically at constant speed? What is the tension in the vertical main cable supporting the piano?

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Answers (1)

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Benjamin Mayo · Answer 1

Ellen will maintain a tension of - 513.274N

Tension in the vertical main cable of the piano is 13.274N.

Explanation:

Using Lami's theorem

T1/sinA1 = T2/sinA2

Where A1 is the total angle at Tension 1 (500N) = 90+15 = 105°

Where A2 is the total angle at Tension 2 = 90+25 = 115°

500/sin 115 = T2 / sin105

T2 = - 513.274N.

T3 (tension in the main cable) is calculated knowing that net Tensional force is zero.

T3 + 500-513.274=0

T3 = 13.274N.