Standard +0.8 This is a two-part statics problem requiring resolution of forces, taking moments about a point, and applying friction inequalities. While the setup is standard (rod against wall), students must carefully handle the geometry with the 60° and 30° angles, choose an appropriate moment point, and then work with the friction constraint μ ≥ F/R. The second part requires understanding that friction can act in either direction and setting up an inequality, which is more sophisticated than routine equilibrium problems.
\includegraphics{figure_2}
A uniform rod \(AB\) of weight \(W\) rests in equilibrium with \(A\) in contact with a rough vertical wall. The rod is in a vertical plane perpendicular to the wall, and is supported by a force of magnitude \(P\) acting at \(B\) in this vertical plane. The rod makes an angle of \(60°\) with the wall, and the force makes an angle of \(30°\) with the rod (see diagram). Find the value of \(P\). [3]
Find also the set of possible values of the coefficient of friction between the rod and the wall. [4]
Take moments for rod about A (A.E.F.): 2P cos 60° = W sin 60° M1 A1
Find P: P = W √3/2 or 0⋅866W A1
Resolve vertically for friction F at A (√ on P): F = W – P cos 30° = W/4 M1 A1√
Resolve horizontally for reaction R at A (√ on P): R = P sin 30° = W√3/4 or 0433W B1√
Answer
Marks
Use F ≤ µR to find values of µ: µ ≥ 1/ √3 or µ ≥ 0⋅577 B1
3
4
[7]
Question 2:
2 | Take moments for rod about A (A.E.F.): 2P cos 60° = W sin 60° M1 A1
Find P: P = W √3/2 or 0⋅866W A1
Resolve vertically for friction F at A (√ on P): F = W – P cos 30° = W/4 M1 A1√
Resolve horizontally for reaction R at A (√ on P): R = P sin 30° = W√3/4 or 0433W B1√
Use F ≤ µR to find values of µ: µ ≥ 1/ √3 or µ ≥ 0⋅577 B1 | 3
4 | [7]
\includegraphics{figure_2}
A uniform rod $AB$ of weight $W$ rests in equilibrium with $A$ in contact with a rough vertical wall. The rod is in a vertical plane perpendicular to the wall, and is supported by a force of magnitude $P$ acting at $B$ in this vertical plane. The rod makes an angle of $60°$ with the wall, and the force makes an angle of $30°$ with the rod (see diagram). Find the value of $P$. [3]
Find also the set of possible values of the coefficient of friction between the rod and the wall. [4]
\hfill \mbox{\textit{CAIE FP2 2010 Q2 [7]}}