The Acceleration of a Sliding Collar on a Shaft

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SUMMARY

The discussion focuses on determining the speed and acceleration of collar C on a shaft mechanism, specifically in terms of variables b, θ, θ-dot, and θ-dot-dot. Participants emphasize the importance of establishing a coordinate system to express the position of collar C relative to the given parameters. The fundamental equation used in the analysis is ΣF=ma, which is critical for solving the dynamics of the mechanism. The conversation highlights the need for clarity in problem-solving approaches when tackling such mechanical systems.

PREREQUISITES
  • Understanding of basic mechanics, specifically Newton's second law (ΣF=ma)
  • Familiarity with kinematics and dynamics of rigid bodies
  • Knowledge of angular motion concepts, including angular velocity (θ-dot) and angular acceleration (θ-dot-dot)
  • Ability to interpret and analyze mechanical diagrams and coordinate systems
NEXT STEPS
  • Research methods for deriving equations of motion for mechanical systems
  • Study the application of polar coordinates in dynamics problems
  • Learn about the relationship between linear and angular motion in mechanical systems
  • Explore examples of similar problems involving sliding collars and shafts
USEFUL FOR

Students and professionals in mechanical engineering, particularly those focusing on dynamics and kinematics of mechanisms, will benefit from this discussion.

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Homework Statement



For the mechanism shown, determine the speed and magnitude of the acceleration of collar C in terms of b, θ, θ-dot, and θ-dot-dot.

Check the attached file for the diagram.

We are given the length b and angle θ.

Homework Equations



ΣF=ma

The Attempt at a Solution



I started conceptualizing this problem right now. However, I don't even know where to start. The mechanism moves in such a way that θ 'closes' to 0 (since the whole thing falls). But how would I go about describing that in terms of 'b' ? It'd be dope to get some help/hints :) I'll post my work as the discussion develops. Thank you :)
 

Attachments

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Hello Ernesto, :welcome:

"Don't know where to start" doesn't pass the PF guidelines :rolleyes:
I'll get chastized for answering anyway instead of pressing the 'report' button :nb).

What coordinate system would be the most convenient ?
How do you express the position of C in terms of ##b## and ##\theta## ?
 

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