Velocity as a function of length

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SUMMARY

The discussion focuses on calculating the velocity of a uniform chain of length 3 meters and mass 6 kilograms as it falls under the influence of gravity. Participants agree that the mass of the chain does not affect the outcome, and the problem should be approached using conservation of energy rather than classical equations for constant acceleration. The key equation to consider is the relationship between potential energy and kinetic energy as the chain falls.

PREREQUISITES
  • Understanding of conservation of energy principles in physics
  • Familiarity with calculus-based physics concepts
  • Knowledge of kinematic equations and their limitations
  • Basic understanding of free fall and gravitational acceleration
NEXT STEPS
  • Study the conservation of energy in falling objects
  • Learn how to derive velocity as a function of time for variable mass systems
  • Explore advanced kinematic equations for non-constant acceleration
  • Investigate real-world applications of chain dynamics in physics
USEFUL FOR

Students in calculus-based physics courses, physics educators, and anyone interested in understanding the dynamics of falling objects and energy conservation principles.

Tombo254
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Homework Statement



A uniform chain of length 3 metres and mass 6 kilograms is held by one end so that the other end
just touches the floor. If the chain is released, find its velocity as a function of the length of chain
still falling. How fast does the end of the chain hit the floor?

Homework Equations





The Attempt at a Solution



Does the mass of the chain even matter, or is it a distraction? This is for a calculus based physics course, but I think it can be solved using classical equations, ie: v=xt+1/2at2.
 
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Hi Tombo254! Welcome to PF! :smile:

(try using the X2 icon just above the Reply box :wink:)
Tombo254 said:
Does the mass of the chain even matter, or is it a distraction?

you're right, it doesn't matter! :smile:
… I think it can be solved using classical equations, ie: v=xt+1/2at2.

mmm … that's only for constant acceleration …

i think you'd better use conservation of energy :wink:​
 


tiny-tim said:
mmm … that's only for constant acceleration …

I'm confused ... the chain is falling under the effect of gravity, right? ... which is constant.:confused:

isnt it because the mass of chain in free fall changes continuously and thus v = u + at is not valid ? :confused:
 

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