Tension in string - hanging block

[tony873004]

Homework Statement

Find the tension in string 1

I don't get the same answer as the solution manual.

My attempt:
The y-component of string 2’s tension must equal the weight of the block.
The x-component of string 2’s tension must equal the tension of string 1.
T1=T2x=T2y/tanθ =23°

solution manual says 34 N.

 

[Doc Al]

My attempt:
The y-component of string 2’s tension must equal the weight of the block.
The x-component of string 2’s tension must equal the tension of string 1.

Good.

T1=T2x=T2y/tanθ =23°

Not sure what you did here (better to write the equations step by step), but I think you found that the tension in string 1 is about 23 N (not degrees!). Sounds right to me.

solution manual says 34 N.

I'd say that was wrong.

 

[tony873004]

...Not sure what you did here (better to write the equations step by step).

tanθ=opposite/adjacent
tanθ=T2y/T2x
tanθ=mg/T2x
T2x=T1=mg/tanθ = 23 N (oops,not degrees!)

Thanks Doc Al! Just wanted to make sure I wasn't crazy!

 

[Doc Al]

tanθ=opposite/adjacent
tanθ=T2y/T2x
tanθ=mg/T2x
T2x=T1=mg/tanθ = 23 N (oops,not degrees!)

Much better.

Thanks Doc Al! Just wanted to make sure I wasn't crazy!

You are welcome.

 

[Nickie]

As a scientist, it is important to carefully analyze the problem and the solution to ensure accuracy and understanding. It is possible that there may be a mistake in the solution manual, or in your calculations. I would recommend double-checking your calculations and also considering any assumptions or simplifications that may have been made in the solution manual. It is also important to consider the units used in the solution manual and ensure they are consistent with the given information. If you are still unsure, it may be helpful to seek guidance from a teacher or peer to review your approach and calculations.