Problem in inertial reference frame

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Discussion Overview

The discussion revolves around a physics problem involving a truck with a pack in its back on a frictionless surface. Participants explore the conditions under which the pack will tip over and the role of forces acting on it, particularly in relation to inertial reference frames and the concept of the center of gravity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant describes the setup of the problem and expresses confusion about the relationship between the normal force and the center of gravity when the pack begins to tip over.
  • Another participant suggests visualizing the pack as a point mass connected to a fulcrum and questions the location of the normal force and center of gravity at the tipping point.
  • A different participant identifies the forces acting on the pack at the moment it begins to tip, noting the application of gravity at the center of gravity and the normal forces at the edges near the fulcrum.
  • One participant proposes that the equivalence principle explains why the resultant normal force must pass through the center of gravity, relating it to the stability of the object under horizontal acceleration.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and interpretations of the forces involved, with some proposing explanations while others remain uncertain. There is no clear consensus on the reasoning behind the normal force's relationship to the center of gravity.

Contextual Notes

Participants discuss the implications of the equivalence principle and the stability of objects, but the discussion does not resolve the underlying assumptions or definitions related to the forces at play.

balest
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Well, in principle, this problem seems very easy but I don't know the exact explanation.Here we go. We have a truck and a pack in its back.The bed of the truck is frictionless and the pack is stopped by a small piece of wood of something like that. The size of the pack is whatever(for instance,base=2m^2, height=1,75m)and its mass is 2kg so the question is what is the minimum acceleration of the truck to turn over the pack. In the frame of the truck is easy for me to solve the problem but I don't know how to solve it in an inertial frame. What I want to know is why the normal force, in the exact moment when the pack begins to turn over, has to pass through the centre of gravity.Why? I'm mystified.
 
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balest said:
Well, in principle, this problem seems very easy but I don't know the exact explanation.Here we go. We have a truck and a pack in its back.The bed of the truck is frictionless and the pack is stopped by a small piece of wood of something like that. The size of the pack is whatever(for instance,base=2m^2, height=1,75m)and its mass is 2kg so the question is what is the minimum acceleration of the truck to turn over the pack. In the frame of the truck is easy for me to solve the problem but I don't know how to solve it in an inertial frame. What I want to know is why the normal force, in the exact moment when the pack begins to turn over, has to pass through the centre of gravity.Why? I'm mystified.
Think of the pack as a point mass connected by a rigid rod to the fulcrum (the pack edge pressing against the block of wood). When the rod passes the vertical, the pack starts to turn over. At that point, where is the normal force? Where is the centre of gravity?

AM
 
In the exact situation when the pack begins to turn over I can see those forces

gravity applied in the center of gravity
horizontal normal force(x) applied in the corner near the piece of wood
vertical normal force(y) applied in the corner near the piece of wood too.

but the point is why the net normal force , that's to say, normal force(x)+normal force(y)=black arrow must go through cg(center of gravity). What is the rule,law or whatever in order to infer that?

In the situation you describe it's quite difficult for me to see the forces.I suppose that the normal force is near the fulcrum and vertical as well as the centre of gravity but I'm not sure.

Andrew Mason said:
Think of the pack as a point mass connected by a rigid rod to the fulcrum (the pack edge pressing against the block of wood). When the rod passes the vertical, the pack starts to turn over. At that point, where is the normal force? Where is the centre of gravity?

AM
 
Ok,now I know the answer.The point is incredibly the "equivalence principle" and the stability of an object. That seems crazy but just think of it. The horizontal aceleration of the truck(plus the gravity downward) is the same than a situation where the truck is inclined in such a way that the resulting force goes through the rear botton edge of the pack, that is to say the fulcrum(in this situation the pack is about to tip over) So that's why the resulting normal force is equivalent to a force going through the center of gravity, because of the equivalence principle,isn't it marvelous?
 

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