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Question Number 18607 by Tinkutara last updated on 25/Jul/17
A block of mass M is pulled vertically  upward through a rope of mass m by  applying force F on-one end of the rope.  What force does the rope exert on the  block?
$$\mathrm{A}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:{M}\:\mathrm{is}\:\mathrm{pulled}\:\mathrm{vertically} \\ $$$$\mathrm{upward}\:\mathrm{through}\:\mathrm{a}\:\mathrm{rope}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{by} \\ $$$$\mathrm{applying}\:\mathrm{force}\:{F}\:\mathrm{on}-\mathrm{one}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rope}. \\ $$$$\mathrm{What}\:\mathrm{force}\:\mathrm{does}\:\mathrm{the}\:\mathrm{rope}\:\mathrm{exert}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{block}? \\ $$
Commented by Tinkutara last updated on 25/Jul/17
Answered by mrW1 last updated on 26/Jul/17
(M+m)a=F−(M+m)g  a=(F/(M+m))−g  force from rope on block is  M(g+a)=(M/(M+m))×F
$$\left(\mathrm{M}+\mathrm{m}\right)\mathrm{a}=\mathrm{F}−\left(\mathrm{M}+\mathrm{m}\right)\mathrm{g} \\ $$$$\mathrm{a}=\frac{\mathrm{F}}{\mathrm{M}+\mathrm{m}}−\mathrm{g} \\ $$$$\mathrm{force}\:\mathrm{from}\:\mathrm{rope}\:\mathrm{on}\:\mathrm{block}\:\mathrm{is} \\ $$$$\mathrm{M}\left(\mathrm{g}+\mathrm{a}\right)=\frac{\mathrm{M}}{\mathrm{M}+\mathrm{m}}×\mathrm{F} \\ $$
Commented by Tinkutara last updated on 26/Jul/17
Thanks Sir!
$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$

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