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sArGe99
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Homework Statement
Prism 1 with bar 2 of mass m placed on it gets a horizontal acceleration [tex]\omega[/tex] directed to the left. At what maximum value of this acceleration [tex]\omega[/tex] will the bar be still stationary relative to the prism, if the coefficient of friction between them [tex]k < cot\alpha[/tex]
Homework Equations
[tex]mg sin \alpha - m \omega cos \alpha[/tex] = Force trying to move the body along the prism.
k ([tex]m\omega sin \alpha + mg cos \alpha[/tex]) = Frictional force.
The Attempt at a Solution
Since the prism is accelerating to the left, the bar experiences a pseudo force [tex]m\omega [/tex] directed to the right. Resolving it has components
[tex]m \omega cos \alpha [/tex] opposed to [tex]mg sin \alpha [/tex] and the component [tex]m\omega sin \alpha [/tex] acting along the direction of [tex]mg cos \alpha[/tex]
At equilibrium, the frictional force equals the force which acts along the prism.
Equating, [tex]mg sin \alpha - m\omega cos\alpha[/tex] = k ([tex]m\omega sin \alpha + mg cos \alpha[/tex])
Further simplifying,
[tex]\omega = \frac {g (sin \alpha - k cos \alpha)}{cos \alpha + k sin \alpha}[/tex]
This is not the correct answer. Can you please point out where I've made a mistake?