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.