Standard +0.3 This is a straightforward moments problem requiring students to set up an equilibrium equation about point P using given forces and the reaction force. While it involves a non-uniform beam (requiring finding the center of mass position), the solution follows a standard M1 approach: take moments about P, use the given reaction force, and solve a single linear equation. The arithmetic is slightly involved but the conceptual demand is routine for M1.
3. A beam \(A B\) has length 15 m and mass 25 kg . The beam is smoothly supported at the point \(P\), where \(A P = 8 \mathrm {~m}\). A man of mass 100 kg stands on the beam at a distance of 2 m from \(A\) and another man stands on the beam at a distance of 1 m from \(B\). The beam is modelled as a non-uniform rod and the men are modelled as particles. The beam is in equilibrium in a horizontal position with the reaction on the beam at \(P\) having magnitude 2009 N. Find the distance of the centre of mass of the beam from \(A\).
M1 for equation in relevant unknown length only; A1 A1 for correct equation (\(-1\) each error, omission of \(g\)'s counts as one error)
\(x = 12.8,\ 13\) (m)
DM1 A1 (5)
DM1 dependent for solving for AG; A1 for 12.8 or 13; SC: if \(M\) used but never found, max M1A0A0M0A0
## Question 3:
$M(X),\ 25g(14-x) + 100g \cdot 12 = 200g \times 6$ | M1 A1 A1 | M1 for equation in relevant unknown length only; A1 A1 for correct equation ($-1$ each error, omission of $g$'s counts as one error)
$x = 12.8,\ 13$ (m) | DM1 A1 (5) | DM1 dependent for solving for AG; A1 for 12.8 or 13; SC: if $M$ used but never found, max M1A0A0M0A0
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3. A beam $A B$ has length 15 m and mass 25 kg . The beam is smoothly supported at the point $P$, where $A P = 8 \mathrm {~m}$. A man of mass 100 kg stands on the beam at a distance of 2 m from $A$ and another man stands on the beam at a distance of 1 m from $B$. The beam is modelled as a non-uniform rod and the men are modelled as particles. The beam is in equilibrium in a horizontal position with the reaction on the beam at $P$ having magnitude 2009 N. Find the distance of the centre of mass of the beam from $A$.
\hfill \mbox{\textit{Edexcel M1 2014 Q3 [5]}}