Standard +0.3 This is a standard M1 moments problem requiring setting up equilibrium equations (sum of forces and taking moments about a point) with one algebraic unknown. While it involves multiple forces and a constraint relationship, the solution follows a routine procedure taught in all M1 courses with no novel insight required—slightly easier than average due to its methodical nature.
A beam \(AB\) has length 6 m and weight 200 N. The beam rests in a horizontal position on two supports at the points \(C\) and \(D\), where \(AC = 1\) m and \(DB = 1\) m. Two children, Sophie and Tom, each of weight 500 N, stand on the beam with Sophie standing twice as far from the end \(B\) as Tom. The beam remains horizontal and in equilibrium and the magnitude of the reaction at \(D\) is three times the magnitude of the reaction at \(C\). By modelling the beam as a uniform rod and the two children as particles, find how far Tom is standing from the end \(B\).
[7]
A beam $AB$ has length 6 m and weight 200 N. The beam rests in a horizontal position on two supports at the points $C$ and $D$, where $AC = 1$ m and $DB = 1$ m. Two children, Sophie and Tom, each of weight 500 N, stand on the beam with Sophie standing twice as far from the end $B$ as Tom. The beam remains horizontal and in equilibrium and the magnitude of the reaction at $D$ is three times the magnitude of the reaction at $C$. By modelling the beam as a uniform rod and the two children as particles, find how far Tom is standing from the end $B$.
[7]
\hfill \mbox{\textit{Edexcel M1 Q4 [7]}}