A uniform plank of wood \(XY\), of mass 1.4 kg, rests with its upper end \(X\) against a rough vertical wall and its lower end \(Y\) on rough horizontal ground. The coefficient of friction between the plank and both the wall and the ground is \(\mu\). The plank is in limiting equilibrium at both ends and the vertical component of the force exerted on the plank by the ground has magnitude 12 N. Find the value of \(\mu\), to 2 decimal places. [8 marks]

Let $R =$ reaction at wall | Resolve horizontally: $R = 12\mu$ | M1 A1 |

Resolve vertically: $12 + \mu R = 1.4g$ | M1 A1 |

Hence $12 + 12\mu^2 = 1.4g$ | $1 + \mu^2 = 1.143$ | $\mu = 0.38$ | M1 A1 M1 A1 | 8 marks

A uniform plank of wood $XY$, of mass 1.4 kg, rests with its upper end $X$ against a rough vertical wall and its lower end $Y$ on rough horizontal ground. The coefficient of friction between the plank and both the wall and the ground is $\mu$. The plank is in limiting equilibrium at both ends and the vertical component of the force exerted on the plank by the ground has magnitude 12 N.

Find the value of $\mu$, to 2 decimal places. [8 marks]

\hfill \mbox{\textit{Edexcel M2  Q4 [8]}}