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A-uniform-rope-of-length-L-and-mass-per-unit-having-one-end-fixed-with-the-ceiling-is-released-from-rest-Find-the-tension-in-the-fixed-end-as-a-function-of-the-distance-travelled-by-the-movable-end




Question Number 23666 by Tinkutara last updated on 03/Nov/17
A uniform rope of length L and mass  per unit λ having one end fixed with  the ceiling is released from rest. Find  the tension in the fixed end as a function  of the distance travelled by the movable  end.
AuniformropeoflengthLandmassperunitλhavingoneendfixedwiththeceilingisreleasedfromrest.Findthetensioninthefixedendasafunctionofthedistancetravelledbythemovableend.
Commented by Tinkutara last updated on 03/Nov/17
Answered by ajfour last updated on 03/Nov/17
    F = ((𝛌gl)/2)(1+((3x)/l)) .
F=λgl2(1+3xl).
Answered by ajfour last updated on 03/Nov/17
Commented by ajfour last updated on 04/Nov/17
mg−F=(dp/dt)               =(d/dt)[(m/l)(((l−x)/2))v]          =(m/(2l))(d/dt)[(l−x)v]    =(m/(2l))[−v^2 +(l−x)g]=(m/(2l))[−2gx−gx+gl]      ⇒   F= mg+(m/(2l))(3gx−gl)                 =((mg)/2)(1+((3x)/l))               F =((𝛌lg)/2)(1+((3x)/l)) .
mgF=dpdt=ddt[ml(lx2)v]=m2lddt[(lx)v]=m2l[v2+(lx)g]=m2l[2gxgx+gl]F=mg+m2l(3gxgl)=mg2(1+3xl)F=λlg2(1+3xl).
Commented by Tinkutara last updated on 04/Nov/17
Thank you very much Sir!
ThankyouverymuchSir!

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