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Equilibrium

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

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A $\\var{W}\\,\\text{N}$ crate is supported by several rope-and-pulley arrangements as shown. Determine for each arrangement the tension in the rope (in N).

", "advice": "

(a)

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$+\\!\\!\\uparrow\\sum F_y=0$: $\\quad$ $2T+W=0,$ $\\quad\\Rightarrow\\quad$ $2T=\\var{W}\\,\\text{N},$ $\\quad\\Rightarrow\\quad$ $T=\\var{W/2}\\,\\text{N}\\quad\\blacktriangleleft$

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(b) Same as (a)

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(c)

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$+\\!\\!\\uparrow\\sum F_y=0$: $\\quad$ $3T+W=0,$ $\\quad\\Rightarrow\\quad$ $3T=\\var{W}\\,\\text{N},$ $\\quad\\Rightarrow\\quad$ $T=\\var{W/3}\\,\\text{N}\\quad\\blacktriangleleft$

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(d) Same as (c)

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(e)

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$+\\!\\!\\uparrow\\sum F_y=0$: $\\quad$ $4T+W=0,$ $\\quad\\Rightarrow\\quad$ $4T=\\var{W}\\,\\text{N},$ $\\quad\\Rightarrow\\quad$ $T=\\var{W/4}\\,\\text{N}\\quad\\blacktriangleleft$

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