solve problem

Question

A  150 lb sign is hanging from the end of a hinged boom supported by a cable inclined at 44°  horizontal. Find the tension in the cable and the compression in the boom.

 

1) The tension is_______________

 

2) The compression in the boom is_____________________

Answer 1

Student Question: A 150 pound sign is hanging from the end of a hinged boom supported by a cable inclined at 44° horizontal. Find the tension in the cable and the compression in the boom.

Important Facts:

Weight of sign: 150 pounds

Cable angle: 44 degrees

Noted Information:

The objects are at rest and experiencing no net force. This means that all forces acting on the system are balanced resulting in no movement or change.

____________________________________________________________________________________

Step1:

From the y-direction equation:

T= sin (44 degrees) = 150

T = 150 divided by sin (44 degrees)

T = 150 divided 0.6947

T = 215.92 pounds

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Step 2:

From the x direction equation:

C = T cos (44 degrees)

C = 215.92 times cos (44 degrees)

C = 215.92 times 0.7193

C = 155.31 pounds

Solution:

The tension in the cable is 215.92 pounds and the compression in the boom is 155.31 pounds.

I hope this information is useful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H. (5/12/2025)