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Recently I encountered a funny thing. Consider the following problem from high school course.
A small grasshopper of mass ##m## sits on a tip of a straw. The straw is a thin homogeneous rod of mass ##M## and of length ##2l##. The straw lies on a smooth horizontal floor.
What smallest initial speed must have the grasshopper to jump to other tip of the straw?
As a rule, people solve this problem assuming that the grasshopper jumps along the straw. Nevertheless, for some range of ##m/M## this is not true: the smallest speed is attained when the grasshopper jumps sideways from the straw and the straw rotates under him.
:)
A small grasshopper of mass ##m## sits on a tip of a straw. The straw is a thin homogeneous rod of mass ##M## and of length ##2l##. The straw lies on a smooth horizontal floor.
What smallest initial speed must have the grasshopper to jump to other tip of the straw?
As a rule, people solve this problem assuming that the grasshopper jumps along the straw. Nevertheless, for some range of ##m/M## this is not true: the smallest speed is attained when the grasshopper jumps sideways from the straw and the straw rotates under him.
:)