Pseudo Forces creates stress....
Its just my thought and I dont know how much right I am about it, so I need you guys to discuss on something like follow:- We all know that stresses on any object there are two equal and opposite forces acting on that object, which creates stresses in it. So there are two forces required for creating stresses and are responsible for strain. Now what if there is no other balancing force acting on it, so only one unbalanced force is acting on it, now this object is accelerating in earth's frame of reference and i am not sure whether or not we can apply the stress equations in this conditions as there is only one force. Now if we go into the frame of reference of that accelerating object, the object is no more accelerating, and there are two forces, out of which one is a pseudo force, so we can easily apply stress equations and find out strain in it, it is as if i hadnt told you the nature or the origin of that pseudo force, i dont know if i am wrong at any place, but do comment on this topic, thanks in advance.....
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Vivek Bhagat
7 years, 3 months ago
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Very nice question. I am always looking for such type of questions. Here's my theory:
The inconsistency in your conclusion arises as a result of treating a group of particles as a single point object.
Image a group of kids standing in a row separated by springs. If you apply force from both the ends of the row the distance among the kids will decrease.
Now, lets give them some acceleration up in space. Take the frame of a reference a cabin which encloses the row of kids all the time. There are two forces acting on every kid in the cabin frame of reference:
One is the force which is making them accelerate.
The other force is the pseudo force.
The distance among the kids won't be decreasing this time.
Why?... Let's take a deep look.
When the kids are not accelerating, suppose we apply a force from both the ends of the row. The distance among the kids will decrease. Technically the kids would be oscillating, just imagine how funny would it look!
Anyway, now lets take a look at kids when they are accelerating. Our frame of reference is cabin. This time, we wouldn't say that these two forces are being applied
one from the back
and the other from the front
because each kid will be treated as a point object with its own forces. There's no extra force from both ends as there were in the previous situation resulting in no stress.
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One thing which I forgot to mention is that in the above example I have assumed that when kids are accelerating the force is not applied from one side of the row. Instead force is uniformly applied on the whole system. In the case as your mentioned here:
The strain - stress equation won't be applied ideally. The first particle of the object would be more closer to the particle next to it as it is responsible for making the whole next bunch of particles accelerate. This is not the case when forces from both the ends are applied. Though I still hold no idea how the strain stress equation will be applied in this single end applied force case!!!
OMG! Can't believe I wrote this. Why am I so intelligent?
I am not pretty sure ....but when you apply the pseudo force...you dont apply it on your frame of reference...but to all the objects in your frame of reference...As I said...not pretty sure,so I reshared it hoping that sum1 does comment on this...Sorry that i couldnt help!!! :(
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Consider a finite rod(having fixed mass) moving on a friction less ground. Let the rod be accelerated with the help of only one force F. Now, consider a element of mass dm of length dl from the other end(opposite end to where force is acting). If the rod hadn't been accelerating then the net elastic force must be zero(as its in equilibrium). But once the force F starts acting, a "extra" tension force acts on that element(to make it move with a common acceleration). All our observations here are in ground frame of reference. Now as this tension force is responsible for disturbing the element it also acts a restoring force. So now you can use young's modulus equation to find the elongation.
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still one doubt remains, its that what will be the value of force that you will use to calculate the stress developed, will it be F only, but then how is this situation any different than the one n which the rod is maintain stable with equal and opposite force
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It won't be F. when u take an element from the opposite end, Net force on that is some T. Since the acceleration of the whole body is same; T = mass * acceleration. After this, only the distribution of mass, is what matters. If its distributed uniformly then u will get a linear relation between mass and tension. Is it fyn now?
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Thanks for explaining the linear function part.....but back to the original argument....does this actually mean pseudo force creates stress??
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There's nothing called pseudo force. Its only an assumed quantity which plays its own role when reference frame is shifted to a non-inertial one. To account for the same observation u get for ground reference frame; you have to include pseudo force. In other words; to get the same value for extension in the rod you have to include pseudo force; so talking like that, it creates stress. Note : I neglected all relativistic effects.
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Thanks for clearing it up....I was silly enough to assume pseudo force as an ACTUAL FORCE.!!!
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That's fyn :) We all do it unknowingly sometimes.
i tried to imagine this whole thing in practical world, considering the object is spring, when u apply a force it will get stretched wont it??? And that is what strain of that object is, what i am not getting is how can we not apply this thing in non-inertial frame of reference
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But in the non inertial frame of reference you will hv to consider the existence of a pseudo force
Guyzz Pseudo force is very much hypothetical like centrifugal force
Your fallacy lies in the fact that in the same problem, you are treating your object once as an extended extensible body, and once as a point object. An extensible extended body gets extended only if the inter-molecular distances of the body increase, i.e., say, if we consider two adjacent molecules A and B of it, then they experience opposite forces so as to increase the distance between them, or in other words, the extending forces are acting on it at different points, say, two ends of the object. Now consider a free fall of such an object. If we are in the object's frame, we will see that every molecule of the object experiences a force acting downward due to gravity, but remains at rest. So, an equal pseudo-force acting upward is imagined to be present, which holds each molecule in its position. As each molecule remains in its position, there is no change of the molecular configuration of the body, and it doesn't get extended. The fallacy you were making is that you were considering that the weight and the pseudo-force are acting at two ends of the body, causing its extension, but now you see, its not so.