Normal Force on an Inclined Plane: Does it Depend on the Coordinate System?

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Discussion Overview

The discussion revolves around the concept of normal force acting on a mass placed on an inclined plane and whether this force is dependent on the choice of coordinate system used for analysis. Participants explore different coordinate systems and their implications on calculating the normal force in both tilted and standard orientations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that the normal force can be expressed as N = MgCos(theta) when using a coordinate system aligned with the incline.
  • Another participant agrees that for a stationary inclined plane, N = mg\cos\theta is correct, but notes that for a coordinate system aligned with the vertical, the angle would be zero, leading to confusion.
  • A participant clarifies that the choice of coordinate system can affect how forces are represented, indicating that forces in the y-direction must balance, leading to the equation N - Mg cos(theta) = 0.
  • One participant challenges the validity of the second equation presented (N = Mg/cos(theta)), suggesting that it arises from a misunderstanding of the forces involved.
  • Another participant expresses regret for their earlier post, indicating a realization of a mistake in their reasoning.
  • A later reply reassures the original poster that confusion over coordinate systems is common and encourages continued inquiry.

Areas of Agreement / Disagreement

Participants generally agree that the normal force is perpendicular to the surface and that the correct expression for the normal force depends on the coordinate system used. However, there is disagreement regarding the validity of the second equation presented, with some participants questioning its correctness.

Contextual Notes

The discussion highlights potential misunderstandings related to the application of different coordinate systems and the resulting equations for normal force. There is an indication that assumptions about force balance may not have been fully considered by all participants.

Who May Find This Useful

This discussion may be useful for students and individuals interested in mechanics, particularly those exploring the effects of coordinate systems on force calculations in physics.

cherian
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I am a new user so if I am violating any rules I apologize


If we have a mass on an inclined plane ,

Does the Normal force depend on Coordinate used. i.e coordinate system along rod( tilted one) and coordinate system in the regular way

I know the answer is " NO" but I get


N= MgCos(theta) for tilted one
and N= Mg/cos(theta) for straight one

Same is happening for a rod rotating about the edge of a table


Thanks in advance
 
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Hi cherian, welcome to PF.

I am not really sure what you are asking here, but no it doesn't matter. If the inclined plane is stationary the you are correct in saying that N = mg\cos\theta where \theta is the angle of inclination . In the second case remember \cos0 = 1 because the plane is inclined at 0 degrees.
Sorry if I have misunderstood your question.
 
Sorry I can't express it very well. The plane is inclined in both cases. The cases that I mention is the choice of coordinate system. We can select a coordinate system in which X is parallel to the the mass and Y is perpendicular to the mass ( the tilted one) or
We can choose X and Y in regular way ( how we draw in regular way in paper)
 
cherian said:
N= MgCos(theta) for tilted one
and N= Mg/cos(theta) for straight one
I assume you are trying to figure out the normal force (which is always perpendicular to the surface) using different coordinate systems.

Taking coordinates parallel and perpendicular is easiest. Forces in the y-direction (perpendicular to the surface) must add to zero: N - Mg cos(theta) = 0. (Your first result.)

Your second equation comes from setting the vertical forces equal to zero: N cos(theta) -Mg = 0. The problem is: The vertical forces do not add to zero! So that equation is bogus.
 
I apologize, there was lack of thinking before I posted it, My bad
 
No need to apologize for asking a question! :smile: The only thing that matters is whether you received a useful answer.

(You'd be surprised at how many students make that same error! Switching coordinate systems can get confusing.)
 

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