forces and tension

**checkmarks** · April 5th 2008, 05:58 PM

A mass (10 kg) hangs from two strings which are attached to the ceiling shown in this picture:
http://i26.tinypic.com/28h0a6v.jpg

What is the tension in each string?

**mr fantastic** · April 5th 2008, 06:16 PM

Originally Posted by checkmarks

A mass (10 kg) hangs from two strings which are attached to the ceiling shown in this picture:
http://i26.tinypic.com/28h0a6v.jpg

What is the tension in each string?

Try using Lami's Theorem: Lami's theorem - Wikipedia, the free encyclopedia

**Mathstud28** · April 5th 2008, 07:21 PM

it in Honors Physics is saying that $\sum{F_x}=0$ and $\sum{F_y}=0$ since this is a statics problem...you set up two equations with two variables based on this and solve them simultaneously...

**earboth** · April 5th 2008, 11:22 PM

Originally Posted by checkmarks

A mass (10 kg) hangs from two strings which are attached to the ceiling shown in this picture:

What is the tension in each string?

The 2 strings must pull together with the same force as the weight of the mass.

Draw the parallelogram of forces. You already know all angles in the marked triangle and the length of the third side. Thus use Sine rule here:

$\frac{|\overrightarrow{F_1}|}{10}=\frac{\sin(40^\c irc)}{\sin(80^\circ)} ~\implies~ |\overrightarrow{F_1}|=10 \cdot \frac{\sin(40^\circ)}{\sin(80^\circ)} \approx 6.527036... kg$ By the way: You are dealing here with forces and therefore the unit kg is very, very inappropriate.

$\frac{|\overrightarrow{F_2}|}{10}=\frac{\sin(60^\c irc)}{\sin(80^\circ)} ~\implies~ |\overrightarrow{F_2}|=10 \cdot \frac{\sin(60^\circ)}{\sin(80^\circ)} \approx 8.79385... kg$

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