How can a vector be resolved into components in various directions?

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Homework Help Overview

The discussion revolves around the resolution of vectors into components, particularly in the context of forces acting on a mass placed on an inclined plane. Participants are exploring how many times a vector can be resolved into components and the implications of choosing different axes for resolution.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the limits of resolving a vector into components, particularly whether components like mg sin(angle) can be further resolved. There is also discussion about the choice of axes and the implications of fixed angles in the context of inclined planes.

Discussion Status

Some participants have offered insights into choosing useful axes for resolution and have noted that original forces can be projected directly in desired directions. There is an ongoing exploration of how to handle projections in directions other than those defined by sine and cosine components.

Contextual Notes

Participants are considering constraints such as the fixed angle of inclination of the wedge and the need for components in specific directions, such as parallel to the horizontal. There is a recognition of the limitations imposed by the geometry of the situation.

sArGe99
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Homework Statement


I just want to get my concepts right again. How many times can a vector be resolved into horizontal and vertical components? In the case of a mass placed on a wedge, the weight of the body can be resolved into mg sin (angle) and mg cos(angle). Can this mg sin(angle) be further resolved and resolved again... Surely it would have components in every direction, then?

Homework Equations



Resolution using sine and cosine functions

The Attempt at a Solution


Again, none of the books really helped me on this
 
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sArGe99 said:

Homework Statement


I just want to get my concepts right again. How many times can a vector be resolved into horizontal and vertical components? In the case of a mass placed on a wedge, the weight of the body can be resolved into mg sin (angle) and mg cos(angle). Can this mg sin(angle) be further resolved and resolved again... Surely it would have components in every direction, then?

Homework Equations



Resolution using sine and cosine functions

The Attempt at a Solution


Again, none of the books really helped me on this

Typically you want to choose a useful axis set. Gravity direction usually makes a fine choice and ⊥ planes make up useful 2nd and 3rd dimensions.

But generally you don't make a lot of different projections of things that are already projections since the original forces can be projected in whatever angles you need directly.
 
But in cases, like the one with an inclined plane the angle of inclination is given, it cannot be changed - say its theta. If we want the projection to be in other directions than what is given by sine and cosine components of theta, what do we do?
For example, mg sin theta acts parallel to the wedge surface and cosine component perpendicular. But what if we need a component parallel to the horizontal?
 
sArGe99 said:
But in cases, like the one with an inclined plane the angle of inclination is given, it cannot be changed - say its theta. If we want the projection to be in other directions than what is given by sine and cosine components of theta, what do we do?
For example, mg sin theta acts parallel to the wedge surface and cosine component perpendicular. But what if we need a component parallel to the horizontal?

I look to the original force wherever possible. Why take sines of cosines if you don't have to?
 

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