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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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.

Physics
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|dw:1436069038362:dw|
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|
so the subsequent vector equations hold: \[\Large \left\{ \begin{gathered} {M_1}{\mathbf{g}} + {{\mathbf{T}}_{\mathbf{1}}} - {{\mathbf{T}}_2} = {\mathbf{0}} \hfill \\ \hfill \\ {M_2}{\mathbf{g}} + {{\mathbf{T}}_{\mathbf{2}}} = {\mathbf{0}} \hfill \\ \end{gathered} \right.\]

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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
scalar*
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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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