It's a 100% standard problem in any basic physics course, and I cannot solve it.

Here's the scenario:

physics problem

What is the tension in the strings (T1 and T2)?

My thoughts were (cos/sin rewritten as cos(60°)=½ or cos(45°)=½√2, for example):

From the x components:

cos(45°) T2 + cos(60°) T1 = 0
T1 = −√2 T2

From the y components:

sin(60°) T1 + sin(45°) T2 = m g
½√3 T1 + ½√2 T2 = m g

But using that as the basis to algebraically get the Ts leads to the wrong solution.

PS: Yes that's a homework (this edX course), but I already have the accepted solution (there is a "Show answer" button when one has exhausted ones attempts), and after this I'll drop the course anyway because it just takes too much time and I'm taking it just for fun.


closed as off-topic by Pranav Hosangadi, John Rennie, Bernhard, Danu, JamalS Jan 11 '15 at 13:21

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It is important to chose a frame of reference which you stick with. In the reference frame with positive X axis towards the right, and positive Y axis straight up, angles are measured from the positive X axis. The first angle is $\theta_1 = 60°$, and the second is $\theta_2 =180°-45°$. So, From the x components: $T_2 \cos{ (180-45)}+T_1 \cos{60} = 0$ from which $T_1 = \sqrt{2}T_2$

It doesn't make a difference in the Y components as $\sin{\theta} = \sin{(180° - \theta)}.$


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