A chain having a length L and weight W rests on a street for which the coefficient of staticfriction is μs. If a crane is used to hoist the chain, determine the force P it applies to the chain if the length of chain remaining on the ground begins to slip when the horizontal component is Px. What

Question

A chain having a length [latex]L[/latex] and weight [latex]W[/latex] rests on a street for which the coefficient of staticfriction is [latex]{ \mu }_{ s }[/latex]. If a crane is used to hoist the chain, determine the force [latex]P[/latex] it applies to the chain if the length of chain remaining on the ground begins to slip when the horizontal component is [latex]{ P }_{ x }[/latex]. What length of chain remains on the ground?

Given:

[latex]L[/latex] = [latex]20[/latex] [latex]ft[/latex]

[latex]W[/latex] = [latex]8[/latex] [latex]\frac { Ib }{ ft }[/latex]

[latex]{ \mu }_{ s }[/latex] = [latex]0.2[/latex]

[latex]{ P }_{ x }[/latex] = [latex]10[/latex] [latex]Ib[/latex]

Accepted Answer

[latex]\sum { { F }_{ x } } =0;\quad -{ P }_{ x }+{ \mu }_{ s }{ N }_{ C }=0[/latex]

[latex]\quad \quad \quad \quad \quad \quad { N }_{ C }=\frac { { P }_{ x } }{ { \mu }_{ s } }[/latex]

[latex]\quad \quad \quad \quad \quad \quad { N }_{ C }=50.00Ib[/latex]

[latex]\sum { { F }_{ y } } =0;\quad { P }_{ y }-WL+{ N }_{ C }[/latex]

[latex]\quad \quad \quad \quad \quad \quad { P }_{ y }=WL-{ N }_{ C } [/latex]

[latex]\quad \quad \quad \quad \quad \quad { P }_{ y }=110.00Ib [/latex]

[latex]\quad \quad \quad \quad \quad \quad P=\sqrt { { P }_{ x }^{ 2 }+{ P }_{ y }^{ 2 } } [/latex]

[latex]\quad \quad \quad \quad \quad \quad P=110Ib [/latex]

The length on the ground is supported by [latex]{ N }_{ C }=50.00Ib[/latex] thus

[latex]\quad \quad \quad \quad \quad \quad L=\frac { { N }_{ C } }{ W } [/latex]

[latex]\quad \quad \quad \quad \quad \quad L= 6.25 ft [/latex]

Question : A chain having a length L and weight W rests on a street for...

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