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Introductory Physics Homework Help
Mass attached to a rope. the rope encounters a nail.
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[QUOTE="Karol, post: 5444712, member: 20512"] [h2]Homework Statement [/h2] M is attached to a rope L and starts from horizontal. the rope hits a nail at distance D. What is m's velocity when it reaches the lowest point. At what minimal distance D should the nail be places so that m will complete a circle round the nail. [ATTACH=full]99213[/ATTACH] [h2]Homework Equations[/h2] Kinetic energy: ##E_k=\frac{1}{2}mv^2## Potential energy: ##E_p=mgh## Centrifugal force: ##F=m\frac{v^2}{r}## [h2]The Attempt at a Solution[/h2] Conservation of energy relative to the lowest point: $$mgL=\frac{1}{2}mv^2\;\rightarrow\; v=\sqrt{2gL}$$ The centrifugal force at the top equals only the weight: $$m\frac{v_2^2}{L-D}=mg\;\rightarrow\;v_2^2=(L-D)g$$ The kinetic energy at the bottom, which equals the initial potential energy, equals the potential and kinetic energy at the top: $$\frac{1}{2}mg(L-D)+2\cdot mg(L-D)=mgL\;\rightarrow\; D=\frac{3}{5}L$$ [/QUOTE]
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Introductory Physics Homework Help
Mass attached to a rope. the rope encounters a nail.
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