## anonymous one year ago Could someone help me with this problem please? about torque and momentum

1. anonymous

2. Michele_Laino

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

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

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

Nicely done @Michele_Laino

6. Michele_Laino

thanks!! @Astrophysics :)

7. rvc

@Michele_Laino is awesome in physics and math :)

8. Michele_Laino

:) @rvc