A lift of total mass M is raised by cables from rest through a height h. The greatest tension which the cables can safely bear is nMg. The maximum speed of lift during its journey if the ascent is to made in shortest time is

Question

Infinity Learn · Accepted Answer

Weight of lift $$=$$ MgMaximum $$tension=nMg$$∴  Maximum acceleration $$=nMg$$−MgM                                                $$=(n$$−$$1)gand$$ maximum retardation $$=$$ gcorresponding $$velocity-time$$ graph for shortest time will be as follows: Here (n$$−$$1)g=vmt1$$ or $$t1=vm(n$$−$$1)g$$    .......$$(1) and $$g=vmt2$$ or $$t2=vmg$$    ......(2)Area$$ under $$v-t$$ graph is total displacement ft.Hence $$h=12t1+t2vm$$  ......$$(3)From$$ $$(1), (2) and (3) we get,$$vm=2ghn$$−$$1n$$

A lift of total mass M is raised by cables from rest through a height h. The greatest tension which the cables can safely bear is nMg. The maximum speed of lift during its journey if the ascent is to made in shortest time is

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