| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Uniform beam on two supports |
| Difficulty | Moderate -0.3 This is a standard M1 equilibrium problem requiring resolution of forces and taking moments about a point. While it involves two equations and some algebraic manipulation, the method is routine and well-practiced: sum of forces = 0 gives the mass, and sum of moments = 0 gives x. The context is straightforward with no conceptual subtleties, making it slightly easier than average for A-level. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Weight \(= 19 - 18 = 1\) N, so mass \(= 1 \div g = 0.102\) kg \(= 102\) g | M1 A1 A1 | |
| (b) M(0): \(1(15) + 18(10) = 11(5) + 8x\) → \(8x = 140\) → \(x = 17.5\) | M1 A1 A1 | |
| (c) Assumed it is a straight line with weight acting at mid-point | B1 | Total: 7 marks |
**(a)** Weight $= 19 - 18 = 1$ N, so mass $= 1 \div g = 0.102$ kg $= 102$ g | M1 A1 A1 |
**(b)** M(0): $1(15) + 18(10) = 11(5) + 8x$ → $8x = 140$ → $x = 17.5$ | M1 A1 A1 |
**(c)** Assumed it is a straight line with weight acting at mid-point | B1 | **Total: 7 marks**A boy holds a 30 cm metal ruler between three fingers of one hand, pushing down with the middle finger and up with the other two, at the points marked 5 cm, 10 cm and $x$ cm and exerting forces of magnitude 11 N, 18 N and 8 N respectively. The ruler is in equilibrium in this position. Modelling the ruler as a uniform rod, find
\includegraphics{figure_1}
\begin{enumerate}[label=(\alph*)]
\item the mass of the ruler, in grams, \hfill [3 marks]
\item the value of $x$. \hfill [3 marks]
\item State how you have used the modelling assumption that the ruler is a uniform rod. \hfill [1 mark]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q1 [7]}}