wire of some mass $M$?

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Apr 27, 2023 at 18:37	comment	added	jalex		@Aakash - I did the effective mass calculation for the catenary shape and you find $1/3$ is the mass fraction at the end of the rope.
Apr 27, 2023 at 18:36	history	edited	jalex	CC BY-SA 4.0	added 1107 characters in body
Apr 27, 2023 at 17:51	comment	added	jalex		So then the effective mass depends on the shape it takes. And the shape isn't defined in this problem. If you do have a shape, then as you move the end with velocity $v_0$, each slice ${\rm d}x$ of the rope must have some velocity $v(x)$ and you find the effective mass from the total kinetic energy of the system $$ \tfrac{1}{2} m_{\rm eff} v_0^2 = \tfrac{1}{2} \int \rho A v(x)^2 {\rm d}x $$ where $\rho$ is the density and $A$ is the section area. Also note that $\rho A = \tfrac{m}{L}$ with mass $m$ and length $L$.
Apr 27, 2023 at 17:43	comment	added	Aakash		What if the rope is kept on a table and then pushed????
Apr 27, 2023 at 16:51	history	edited	jalex	CC BY-SA 4.0	added 655 characters in body
Apr 27, 2023 at 16:44	history	edited	jalex	CC BY-SA 4.0	added 655 characters in body
Apr 27, 2023 at 16:32	history	answered	jalex	CC BY-SA 4.0