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anonymous

  • one year ago

two object arre connected vertically by ligth string. the string connecting 4 kg object (upper) and 5 kg (lower) a) determine the tension in the upper object T1 and lower object T2. if the system is equilibrium.

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  1. anonymous
    • one year ago
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    |dw:1436069038362:dw|

  2. Michele_Laino
    • one year ago
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    since our system is at equilibrium, we can apply the first law of mechanics. The external forces acting on each object are like below: |dw:1436076149316:dw|

  3. Michele_Laino
    • one year ago
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    so the subsequent vector equations hold: \[\Large \left\{ \begin{gathered} {M_1}{\mathbf{g}} + {{\mathbf{T}}_{\mathbf{1}}} - {{\mathbf{T}}_2} = {\mathbf{0}} \hfill \\ \hfill \\ {M_2}{\mathbf{g}} + {{\mathbf{T}}_{\mathbf{2}}} = {\mathbf{0}} \hfill \\ \end{gathered} \right.\]

  4. Michele_Laino
    • one year ago
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    Now using the reference system in my drawing, namely the z-axis, we get the subsequent scalars equations: \[\Large \left\{ \begin{gathered} - {M_1}g + {T_1} - {T_2} = 0 \hfill \\ \hfill \\ {M_2}g + {T_2} = 0 \hfill \\ \end{gathered} \right.\] Please solve that algebraic system for the tensions T_1 and T_2

  5. Michele_Laino
    • one year ago
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    scalar*

  6. anonymous
    • one year ago
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    thank you so much!!!

  7. Michele_Laino
    • one year ago
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    Sorry I have made an error of sign, here is the right system: \[\Large \left\{ \begin{gathered} - {M_1}g + {T_1} - {T_2} = 0 \hfill \\ \hfill \\ - {M_2}g + {T_2} = 0 \hfill \\ \end{gathered} \right.\]

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