How Is the Tension Calculated in the Main Cable Supporting a Piano?

AI Thread Summary
The discussion revolves around calculating the tension in the main cable supporting a 500 kg piano being lowered by a crane, with Bob and Ellen stabilizing it using ropes. Bob's rope exerts a tension of 500 N at a 15-degree angle below horizontal, while Ellen's rope has been calculated to exert 533 N at a 25-degree angle below horizontal. Participants emphasize the importance of analyzing the horizontal components of the tensions in both ropes, noting that the piano does not accelerate horizontally, which implies that the horizontal forces must balance. The tension in the main cable can be derived from the vertical forces acting on the piano, taking into account the weight of the piano and the vertical components of the tensions in the ropes. Understanding these forces is crucial for determining the overall tension in the main cable.
skinard360
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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. Ellen's rope pulls toward the right, 25 degrees below horizontal.

What is the tension in the main cable supporting the piano?

I found that the tension in Ellens rope was 533 N but I have no idea how to figure out the tension force in the main cable...can anybody help?? :confused:
 
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skinard360 said:
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. Ellen's rope pulls toward the right, 25 degrees below horizontal.

What is the tension in the main cable supporting the piano?

I found that the tension in Ellens rope was 533 N but I have no idea how to figure out the tension force in the main cable...can anybody help?? :confused:
What can you say about the horizontal components of the tension in the two ropes? (Hint:Does the piano accelerate horizontally?)

AM
 
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