How does force decomposition help us understand the physics of friction?

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Discussion Overview

The discussion revolves around the concept of force decomposition in the context of understanding friction and equilibrium in physics. Participants explore the mathematical representation of forces, particularly the weight of an object and its components, and how these relate to frictional forces.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants express confusion about the decomposition of the weight vector (W) into its components, the normal force (Fn) and the frictional force (-Fr), questioning whether this introduces forces that do not exist.
  • Others clarify that decomposing forces is a valid mathematical approach, emphasizing that it does not add or remove forces but rather describes the same force in different terms.
  • There is a discussion about the magnitudes of the components, with some participants noting that the sum of the magnitudes of the components can exceed the magnitude of the original force, leading to questions about the significance of this observation.
  • Participants highlight the importance of treating forces as vectors, noting that direction plays a crucial role in vector addition, and that adding magnitudes without considering direction does not yield meaningful results.

Areas of Agreement / Disagreement

Participants generally agree on the validity of force decomposition but express differing views on the implications of the magnitudes of the components compared to the original force. The discussion remains unresolved regarding the significance of these observations.

Contextual Notes

There are limitations in the clarity of the diagram referenced, and assumptions about the equilibrium state of the block are made but not fully explored. The discussion also does not resolve the implications of the relationship between the magnitudes of the components and the original force.

ErikD
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[PLAIN]http://upload.wikimedia.org/wikipedia/en/7/7a/Friction.png

I can decompose W to get Fn and -Fr.

Fn = W cos([tex]\theta[/tex])
-Fr = W sin([tex]\theta[/tex])

I know I'm allowed to decompose forces like that but I'm a bit confused as to why. Cause |Fn| + |Fr| > |W| (for the angle in this picture). So by decomposing W am I not introducing force that isn't there?
 
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ErikD said:
I can decompose W to get Fn and -Fr.

Fn = W cos([tex]\theta[/tex])
-Fr = W sin([tex]\theta[/tex])
I don't quite understand your diagram. What's Fr? Is the block in equilibrium?

You can certainly write any vector in terms of its components.

I know I'm allowed to decompose forces like that but I'm a bit confused as to why. Cause |Fn| + |Fr| > |W| (for the angle in this picture).
I don't understand the significance of adding the magnitudes of these components. The sum of the magnitudes of the components will be greater than the magnitude of the vector itself. So?
So by decomposing W am I not introducing force that isn't there?
No. You're just describing the same force in a different way. Nothing's been added or removed.
 
Sorry I should have been a bit more clear. Yes the block is in equilibrium. Fr is the force of friction. Fr = W sin([tex]\theta[/tex]) so the block isn't moving.

Isn't the magnitude of a force the amount of Newtons the force is strong? So don't the magnitudes of the components have more Newtons than the force itself?
 
ErikD said:
Sorry I should have been a bit more clear. Yes the block is in equilibrium. Fr is the force of friction. Fr = W sin([tex]\theta[/tex]) so the block isn't moving.
OK.

Isn't the magnitude of a force the amount of Newtons the force is strong?
Sure.

So don't the magnitudes of the components have more Newtons than the force itself?
You mean "Is the sum of the magnitudes of the components greater than the magnitude of the force itself?" Sure! So what?

Note that the components are in different directions--they are perpendicular to each other--so adding the magnitudes has no special meaning. Only adding them as vectors has any meaning.

The moral is that you must treat force as a vector, not a scalar. Given two vectors (in this case, the components of the weight) you must add them as vectors to find the total. You can't just add the magnitudes. Direction matters! (Take two 10 N forces. Depending on their directions, the total of those forces can be anything from 0 N to 20 N. Adding the magnitudes only makes sense if they point in the same direction.)
 
Thanks, that clears up my confusion.
 

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