How does the movement of A affect the movement of B?

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SUMMARY

The discussion focuses on the relationship between the movements of two points, A and B, connected by a rope, specifically how the horizontal movement of A affects the vertical movement of B. The correct relationship is established as Xb = Xa * cos(30), where Xb is the downward movement of B and Xa is the rightward movement of A. The participants clarify that the length of the rope remains constant, leading to the conclusion that differentiation is necessary to analyze the relationship between their accelerations.

PREREQUISITES
  • Understanding of basic trigonometry, specifically cosine functions.
  • Knowledge of kinematics and the relationship between displacement and acceleration.
  • Familiarity with the concept of constraints in mechanical systems.
  • Ability to perform differentiation in calculus.
NEXT STEPS
  • Study the principles of kinematics in constrained systems.
  • Learn about differentiation of trigonometric functions, particularly cos(theta).
  • Explore the application of the Pythagorean theorem in mechanical systems.
  • Investigate the implications of constant length constraints in physics problems.
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Students studying physics, particularly those focusing on mechanics and kinematics, as well as educators looking for examples of constraint relationships in physical systems.

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Homework Statement



http://s284.photobucket.com/albums/ll12/toluun/?action=view&current=IMAG0004.jpg

Here is a picture of the problem at hand. I know how to solve the problem however the only thing I don't understand is the relationship between A and B. This means that if A moves to the right 1ft how far will B move downward?

Homework Equations



I know how to solve the problem however the only thing I don't understand is the relationship between A and B. This means that if A moves to the right 1ft how far will B move downward?


The Attempt at a Solution



I first tried thinking that if A moved 1 ft to the right the change in B would be the length of the rope covered. So Xb(change in mass b)= Xa/cos(30).

However this is incorrect I have the solution and the relationship is Xb = Xa * cos(30)
can anyone explain this?
 
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You know that r*cos(theta)=Xa and r+Xb=constant (said constant being the length of the rope). You can figure out the relationship between Xa and Xb by substitution.
 
ideasrule said:
You know that r*cos(theta)=Xa and r+Xb=constant (said constant being the length of the rope). You can figure out the relationship between Xa and Xb by substitution.

I have a question, since we are looking for the relationship between the accelerations, we have to differentiate to get it. But when we do, do we differentiate the cos(theta)?
 

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