Equilibrium problem: Calculate the tension of each cord

AI Thread Summary
The discussion focuses on calculating the tension in cords using trigonometric relationships. A participant emphasizes the efficiency of using a force triangle and the sine rule for quicker solutions, noting that this method reduces errors compared to others. They also point out that a unit was omitted in a final answer, resulting in a loss of marks. Additionally, the importance of correctly drawing force polygons is highlighted, as they help visualize forces in balance and determine resultant forces. Overall, the conversation aims to improve problem-solving techniques in physics.
TheePhysicsStudent
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Homework Statement
Was practising an equilibrium problem (and i have done quite a few like this one before and got them right) and I am unsure Where i have went wrong here
Relevant Equations
t1v + t2v = 2.8
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The question
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What I did
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The answer
 
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##\frac{\cos\theta}{\sin\theta}=?##
 
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Not ##\tan## :smile:
(slow typist)
 
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Also, $$\begin{align} & T_2\frac{\cos60^{\circ}\cos40^{\circ}}{\sin40^{\circ}}+
T_2\sin60^{\circ}=T_2\left(\frac{\cos60^{\circ}\cos40^{\circ}+\sin60^{\circ}\sin40^{\circ}}{\sin40^{\circ}}\right) \nonumber \\
& =T_2\frac{\cos(60^{\circ}-40^{\circ})}{\sin40^{\circ}} =T_2\frac{\cos20^{\circ}}{\sin40^{\circ}}.\nonumber
\end{align}$$
 
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TheePhysicsStudent said:
A couple of things worth noting...

1. If you draw the force-triangle and use the sine rule, the problem takes only a few lines of simple working. (It’s a lot quicker and less error-prone than the method you used.)

2. You have forgotten the unit in your final answer - lose one mark!
 
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To avoid any confusion, by 'force-triangle' (in Post #5) I meant this...
triangle.gif
 
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Steve4Physics said:
To avoid any confusion, by 'force-triangle' (in Post #5) I meant this...
View attachment 339715
Wow thanks, I think this information may help speed time in lots of calculations i do
 
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TheePhysicsStudent said:
Wow thanks, I think this information may help speed time in lots of calculations i do
Just in case it is not clear, when drawing a force polygon of forces in balance, the arrows join head to tail, as in @Steve4Physics' drawing.
You can also use them to find the resultant of a system of forces. In that case the resultant completes the polygon but its arrow is reversed.
 
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