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I was always confused on how we define the directions of the forces in equilibrium problems.
Let's say I have a simple structure: enter image description here

In this case, I assumed that Ray and Rcy are pointing up to counter that 10KN forces.
enter image description here

However, when I assume that Ray is pointing down and Rcy is pointing up, it changes the answer for Ray.

I've also heard a lot that if you assume the wrong direction of the force it will come up as a negative value.
As you can see here if I assume a different direction, it actually comes up with a totally different value.

Am I missing something? Any help will be greatly appreciated!

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    $\begingroup$ First, please you MathJax to typeset you math. For instance $\sum_i M_i = 0$ will set as $\sum_i M_i = 0$, while using double dollar signs at both ends will typeset it as a bock equation (on it's own line and centered). $\endgroup$ – dmckee Jun 3 '17 at 0:41
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    $\begingroup$ Second you might want to try exhibit exactly what you mean by "As you can see here if I assume a different direction, it actually comes up with a totally different value", because I'm not sure you are visualizing the correct result. $\endgroup$ – dmckee Jun 3 '17 at 0:42
  • $\begingroup$ I get the same magnitude and direction either way. You probably have a sign error in your unseen (2nd) result. If you get a discrepancy like this in calculations involving vectors, it's always a good idea to check your signs 3 or 4 times before asking for outside assistance. $\endgroup$ – Bill N Jun 3 '17 at 2:16
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Equilibrium means to make the system stay at rest. i.e., to make it stay as it is. The way you have defined the forces to attain equilibrium is correct (as in the image) as you can attain both linear and angular equilibrium. Linear equilibrium is obtained if the sum of the forces( i.e., the net force ) in each direction is zero. And angular equilibrium, if the net torque is zero.

But, taking $ Ray $ and $ Rcy $ to be in opposite direction can assume linear equilibrium if :

1) $ Ray + 10= Rcy $ if $ Ray $ is downwards and $ Rcy $ is upwards.

2) $ Rcy + 10 = Ray $ if its vice versa.

But, both the above two cases won't satisfy angular equilibrium as the net torque won't be zero.

Taking both forces to be downwards won't satisfy both equilibriums.

So, you have to define your forces in such a way that they ensure the system to attain overall equilibrium. So, the only way is as you have taken in the image above.

Of course you will get different values as you change the direction of each force as your main concern is to sustain equilibrium and the net force in one direction has to be canceled out by that force that is in the opposite direction.

" $ Ray $ is pointing down and $ Rcy $ is pointing up, it changes the answer for $ Ray $." This is because, in the earlier case the 10$ N $ force was cancelled out by $ Ray $ and $ Rcy $ together but when $ Ray $ is pointing down and $ Rcy $ is pointing up the net force of 10$ N $ and $ Ray $ has to be cancelled out by $ Rcy $ alone and hence $ Rcy $ has to be greater in magnitude $.

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  • $\begingroup$ Thank you for such a clear explanation! Now it finally makes sense. My mistake was that I completely forgot about angular equilibrium... $\endgroup$ – student123 Jun 3 '17 at 18:57

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