For a block moving on a surface(due to some external force acting at the topmost point), if possible, the normal force shifts forward to maintain rotational equilibrium(net torque=0). Why does this happen? Why is rotational equilibrium preferred by nature?
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Note: the answer on a related question https://physics.stackexchange.com/q/314729/ does not answer my question. It simply states that because the block is not tumbling, normal force must've shifted to counteract any torque on it. I want to know why this happens – xasthor Sep 05 '17 at 07:17
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Why does this happen?
Because, otherwise the floor would break...
A normal force is nothing more than a "holding up" force. The floor doesn't care about balancing out forces or about balancing out torques. It just cares about not breaking.
When you push sideways at the top of the box, then not only does the weight pull down but also the torque tries to make the corner move downwards (and the opposite corner upwards). So this corner now pushes more downwards than before (and the opposite corner less than before).
There is a normal force at every contacting point, and the one at the corner now increases (while the one at the opposite corner decreases), and you have a gradual change in the normal force over the contacting surface. In many situations it is not easy to work with such a gradual spread of normal forces - so they are summed up into one normal force and averaged into acting at one point (in the same way that you sum up gravity in each particle and call it weight and then average that into pulling in just the centre of mass). This point will then shift leftwards, if there is more total normal force on the left side.
Why is rotational equilibrium preferred by nature?
Were there no floor, then the torque would not be balanced. And no rotational equilibrium would be achieved. So it is not accurate to say that "rotational equilibrium" is preferred by nature. Rotational equilibrium (as well as linear/translational equilibrium of course) just happens to be the case when things are not moving.
Steeven
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Why are the only two options: a) the floor breaking b) rotational equilibrium? Why couldn't the block simply tumble, like it does once normal reaction shifts completely to the right? – xasthor Sep 05 '17 at 18:22
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@xasthor Tumbling over its corner would require the centre-of-mass to be lifted. Naturally this does not happen as nothing here adds any energy, which would be required for the object to gain potential energy. – Steeven Sep 11 '17 at 16:17
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@xasthor Do you mean the normal force? This is not correct. First of all, the normal force can only act during contact - contact is lost as soon as the object start lifting the slightest. Normal force will never be able to lift a surface off, since it simply disappears should that happen. Secondly, the normal force is a force that always adjusts to exactly equalize what it has to hold back against. It will never provide excess lift - never excess energy - so it will never be able to lift anything, it will only ever stop and hold back against forces to balance out whatever come at it. – Steeven Sep 11 '17 at 18:01
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@steeven I'm talking about the external force that is pushing the block – xasthor Sep 11 '17 at 18:11
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@xasthor Oh, I get your point now finally. Well that force can indeed make the block tumble. If the friction is tough enough of course. But if this happens and the tumbling really starts, then we agree that the whole weight will be put on the corner, right? So the normal force will be on this corner, right? Which means that the normal force must have moved from the centre, which is the rest-case, to the corner and on the way it has been in-between - shifting more and more sideways. This "more and more sideways" shifting is the situation I am talking about. The tumbling is the extreme of that. – Steeven Sep 11 '17 at 20:56
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@Steeven Oh okay I get it. That makes sense, however I don't see the need for friction since the force as I stated in the question is acting on the topmost point, already producing a torque. – xasthor Sep 11 '17 at 22:34