| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Block on rough horizontal surface – accelerating (finding acceleration or applied force) |
| Difficulty | Moderate -0.8 This is a straightforward M1 mechanics question testing basic application of Newton's second law and friction. Part (a) is direct F=ma, part (b) adds friction requiring F-μR=ma with R=Mg, and part (c) is simple algebraic substitution. All steps are standard textbook exercises with no problem-solving insight required, making it easier than average. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03r Friction: concept and vector form3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(F = Ma\), so \(F = 3M\) | M1 A1 | |
| (b) \(F - \mu g = 3M\) | \(F = M(3 + \mu g)\) | M1 A1 |
| (c) \(3 + \mu g = \frac{1}{2}g\) | \(\mu = \frac{1}{2} - \frac{3}{g} = 0.194\) | M1 A1 A1 |
(a) $F = Ma$, so $F = 3M$ | | M1 A1
(b) $F - \mu g = 3M$ | $F = M(3 + \mu g)$ | M1 A1
(c) $3 + \mu g = \frac{1}{2}g$ | $\mu = \frac{1}{2} - \frac{3}{g} = 0.194$ | M1 A1 A1 | **7 marks**A force of magnitude $F$ N is applied to a block of mass $M$ kg which is initially at rest on a horizontal plane. The block starts to move with acceleration 3 ms$^{-2}$. Modelling the block as a particle,
\includegraphics{figure_4}
\begin{enumerate}[label=(\alph*)]
\item if the plane is smooth, find an expression for $F$ in terms of $M$. [2 marks]
\end{enumerate}
If the plane is rough, and the coefficient of friction between the block and the plane is $\mu$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item express $F$ in terms of $M$, $\mu$ and $g$. [2 marks]
\item Calculate the value of $\mu$ if $F = \frac{1}{2}Mg$. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [7]}}