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anonymous

  • one year ago

Could someone help me with this problem please? about torque and momentum

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  1. anonymous
    • one year ago
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  2. Michele_Laino
    • one year ago
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    here we have to apply the fundamental equations of mechanics, namely: \[\Large \left\{ \begin{gathered} {{\mathbf{F}}_{\mathbf{A}}} + {{\mathbf{F}}_{\mathbf{B}}} + M{\mathbf{g}} = {\mathbf{0}} \hfill \\ {\mathbf{GA}} \times {{\mathbf{F}}_{\mathbf{A}}} + {\mathbf{GB}} \times {{\mathbf{F}}_{\mathbf{B}}} = {\mathbf{0}} \hfill \\ \end{gathered} \right.\] please note that, those are vector equations.

  3. Michele_Laino
    • one year ago
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    now using a refernece system in the drawing: |dw:1435473234858:dw| we can write these subsequent scalar equations, which are equivalent to those vector ones: \[\Large \left\{ \begin{gathered} {F_A}\cos \theta + {F_B}\cos \theta - Mg\cos \theta = 0 \hfill \\ - {F_A}\sin \theta - {F_B}\sin \theta + Mg\sin \theta = 0 \hfill \\ {F_A}\cos \theta - {F_A}\sin \theta - {F_B}\cos \theta - {F_B}\sin \theta = 0 \hfill \\ \end{gathered} \right.\]

  4. Michele_Laino
    • one year ago
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    please, note that the third equation, solve your problem. As homework, you can check these other 2 equations: \[\Large \left\{ \begin{gathered} {F_A} = \frac{{1 - \tan \theta }}{2}Mg \hfill \\ \hfill \\ {F_B} = \frac{{1 + \tan \theta }}{2}Mg \hfill \\ \end{gathered} \right.\] where M is the mass of our object, and g is the gravity, namely g=9.81 m/sec^2, or g=32 feet/sec^2

  5. Astrophysics
    • one year ago
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    Nicely done @Michele_Laino

  6. Michele_Laino
    • one year ago
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    thanks!! @Astrophysics :)

  7. rvc
    • one year ago
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    @Michele_Laino is awesome in physics and math :)

  8. Michele_Laino
    • one year ago
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    :) @rvc

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