Question

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

Answer 1

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.

Answer 2

now using a refernece system in the drawing:

we can write these subsequent scalar equations, which are equivalent to those vector ones:
\[\Large \left\{ \begin{gathered}
{F_A}\cos \theta + {F_B}\cos \theta - Mg\cos \theta = 0 \hfill \\
- {F_A}\sin \theta - {F_B}\sin \theta + Mg\sin \theta = 0 \hfill \\
{F_A}\cos \theta - {F_A}\sin \theta - {F_B}\cos \theta - {F_B}\sin \theta = 0 \hfill \\
\end{gathered} \right.\]

Answer 3

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

Answer 4

Nicely done @Michele_Laino

Answer 5

thanks!! @Astrophysics :)

Answer 6

@Michele_Laino is awesome in physics and math :)

Answer 7

:) @rvc