Velocity in certain direction[components]

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Discussion Overview

The discussion revolves around the relationship between the velocity of a block being dragged along a surface and the velocity of the string pulling it, specifically addressing the use of trigonometric functions in this context. Participants explore the components of velocity in relation to angles and the geometry of the situation.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question why the horizontal velocity of the block M is expressed as v/sinθ instead of vsinθ, suggesting a need for clarification on the relationship between the string's velocity and the block's velocity.
  • One participant proposes that to understand the relationship, one should consider the right triangle formed by the block and the string, indicating a geometric approach to the problem.
  • Another participant expresses understanding of the previous explanation but raises a question about the applicability of the cosine function in this scenario, referencing the typical use of vcosθ for vector components.
  • It is noted that the block's velocity in the direction of the string must equal the rate at which the string is pulled, leading to the equation VB sinθ = v.

Areas of Agreement / Disagreement

Participants express differing views on the correct application of trigonometric functions to describe the velocities involved, indicating that the discussion remains unresolved with multiple competing interpretations.

Contextual Notes

There are assumptions about the geometry of the situation that may not be fully articulated, and the discussion relies on the definitions of velocity components in relation to angles without a consensus on their application in this specific case.

anigeo
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could you please tell me why the velocity of the block M along the horizontal direction is v/sinθ and not vsinθ as in the case of components of vectors?
 

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anigeo said:
could you please tell me why the velocity of the block M along the horizontal direction is v/sinθ and not vsinθ as in the case of components of vectors?
If I understand your diagram (the block is being dragged by the string along the surface), v is the rate at which the string is being pulled. To relate the speed of the block along the surface to the rate at which the string moves, consider the right triangle formed by the block and the string. Let x be the horizontal distance from block to pulley and z be the length of string between block and pulley. How can you relate those quantities?
 
ok i understand what u say. actually this is also what i thought.so thanks.
but while taking the component of a vector along a direction θ from it we write vcosθ if v is the vector.why is it not applicable here?
 
anigeo said:
but while taking the component of a vector along a direction θ from it we write vcosθ if v is the vector.why is it not applicable here?
The block moves along the horizontal. It's the component of the block's velocity (VB) in the direction of the string that must equal the rate at which the string is pulled:
VB sinθ = v
 

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