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Three point masses m, 2m and m, connected with ideal spring (of spring constant k) and ideal string as shown in the figure, are placed on a smooth horizontal surface At t=0, three constant forces F, 2F and 3F start acting on the point masses m, 2m and m respectively, as shown in figure. Find the maximum extension in the spring |
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Answer» `(2F)/(m)`  `rArr F-kx=ma_(1)rArr a_(1)=(F-kx)/(m)`….(`1`)  `rArr T-kx-2F=2ma_(2)`……(`2`)  `rArr3F-T=ma_(2)`.....(`3`) With the help of EQUATIONS (`2`) and (`3`), we have `F=kx=3ma_(2)rArr(F-kx)/(3m)=a_(2)`.......(`4`) With the help of equations (`1`) and (`4`), we have `veca_(12)=veca_(1)-veca_(2)=a_(1)(-HATI)-a_(2)(hati)=(a_(1)+a_(2))(hati)` `V_(12)(dV_(12))/(dx)=a_(12)=(4(F-kx))/(3m)rArrint_(0)^(0)V_(12)dV_(12)=(4)/(3m)int_(0)^(x)(F-kx)dx` `rArr0=(4)/(3m)[Fx-(kx^(2))/(2)]rArrX_(max)=(2F)/(k)` Second method : System is EQUIVALENT to Because Above system behaves as single unit ` |
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