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The question itself:

A modern art sculptor anchors 1 meter of a cast iron pole in the ground and leaves 3 meters of the pole sticking out of the ground at a 60° angle. The owner of the metal shop told him that the pole is rated to withstand up to 9000 Nm of torque before it bends. If the sculptor decides instead to hang a 100 kg aluminum pheasant from the pole in the previous problem, what is the net torque on the pole?

The "Correct" answer (since it's all multiple choice and online) is 0Nm, but for the life of me I can't figure out why there isn't any net torque when the pole has something hanging on the end.

Am I missing something incredibly basic, or was the wrong answer input as the correct one?

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Is the pole rotating? If not, maybe there is more than one source of torque ("net torque"). But this is something of a gotcha answer regarding the definition of "net torque" and supplying irrelevant details. –  Rex Kerr Jul 9 '13 at 20:01
    
@RexKerr The pole is not rotating. And you just knocked something loose in my head... it's in the ground, so the dirt itself is providing the other Force required to counteract the additional weight. Thanks! –  MCM Jul 9 '13 at 20:12
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2 Answers

up vote 4 down vote accepted

So remember that because torque is the cross product, we know that it is $rF\cos\theta$. So you can use this to calculate how much torque the pole is feeling. So it is r=3m, F = mg(~1000 N). And $\theta$ is 60. So the torque the pole feels is 3*1000*cos(60) ~ 1500 Nm. The pole can withstand 9000 Nm. Therefore it does not bend. So there is 0 net torque!

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Figured it out thanks to Rex Kerr's comment. The dirt the pole is sitting in is providing a counter Force to prevent the pole from moving, resulting in a net Torque of 0.

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Note that this is only true if the pole is strong enough to not bend. If it bends, then the torque is not zero on the whole pole! So you do have a calculation to do. –  Rex Kerr Jul 9 '13 at 20:21
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