Standard +0.3 This is a standard mechanics problem involving moments about a hinge with a uniform rod. Students need to find the normal reaction and deduce tension equals weight, then verify the angle relationship - straightforward application of equilibrium conditions with minimal algebraic complexity. Slightly easier than average as it's a guided multi-part question with clear structure.
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\includegraphics[max width=\textwidth, alt={}, center]{f8961f84-c080-4407-a178-45b76f200111-3_561_606_260_767}
A uniform rod \(A B\) has mass \(m\) and length \(2 d\). The rod rests in equilibrium on a smooth peg \(C\), with the end \(A\) resting on a rough horizontal plane. The distance \(A C\) is \(2 a\) and the angle between \(A B\) and the horizontal is \(\alpha\), where \(\cos \alpha = \frac { 3 } { 5 }\). A particle of mass \(\frac { 1 } { 2 } m\) is attached to the rod at \(B\) (see diagram). Find the normal reaction at \(A\) and deduce that \(d < \frac { 25 } { 6 } a\).
The coefficient of friction between the rod and the plane is \(\mu\). Show that \(\mu \geqslant \frac { 8 d } { 25 a - 6 d }\).
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\includegraphics[max width=\textwidth, alt={}, center]{f8961f84-c080-4407-a178-45b76f200111-3_561_606_260_767}
A uniform rod $A B$ has mass $m$ and length $2 d$. The rod rests in equilibrium on a smooth peg $C$, with the end $A$ resting on a rough horizontal plane. The distance $A C$ is $2 a$ and the angle between $A B$ and the horizontal is $\alpha$, where $\cos \alpha = \frac { 3 } { 5 }$. A particle of mass $\frac { 1 } { 2 } m$ is attached to the rod at $B$ (see diagram). Find the normal reaction at $A$ and deduce that $d < \frac { 25 } { 6 } a$.
The coefficient of friction between the rod and the plane is $\mu$. Show that $\mu \geqslant \frac { 8 d } { 25 a - 6 d }$.
\hfill \mbox{\textit{CAIE FP2 2014 Q4}}