| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2022 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Single angled force - find limiting friction or coefficient |
| Difficulty | Moderate -0.3 This is a standard M1 friction problem with two routine parts: (a) resolving forces to check if limiting friction is exceeded, and (b) finding the force at limiting equilibrium. Both require straightforward application of F=μR with resolution at 30°, making it slightly easier than average for A-level but still requiring careful method. |
| Spec | 3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((\uparrow)\ R = 5g - 14\sin30°\) | M1 A1 | M1: correct no. of terms, condone sin/cos confusion and sign errors. A1: correct equation in \(R\) only |
| \(R = 42\ \text{(N)}\) | A1 | Correct value (seen or implied) |
| Max Friction \(= \frac{3}{7}\times42 = 18\ \text{(N)}\) | M1 | Use of \(F=\frac{3}{7}R\) with their \(R\) substituted. 18 only with no working cannot score this M mark |
| Horiz component of \(P = 14\cos30° = 12.124\ldots\) and \(12 < 18\) (their max friction). Must be comparing with maximum friction; 'maximum' must have been clearly stated somewhere. N.B. M0 if they state or imply friction acting on block is 18 N | M1 | Condone sin/cos confusion |
| Friction \(= 12\) or better (N) and block doesn't move | A1 | cao and any equivalent correct statement and justification |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((\uparrow)\ P\sin30° + S = 5g\) | M1A1 | M1: correct no. of terms, condone sin/cos confusion and sign errors. A1: correct equation |
| \((\rightarrow)\ P\cos30° = \frac{3}{7}S\) (Allow M1A0 if they use max friction from (a), or \(\frac{3}{7}\times\text{wrong value for }S\), allow M1A0 for \(P\cos30°=F\)) | M1A1 | M1: correct no. of terms, condone sin/cos confusion and sign errors. A1: correct equation |
| Solve for \(P\) | DM1 | Dependent on both M marks; must be solving two equations in \(P\) and one other unknown |
| \(P = 19\) or \(19.4\ \text{(N)}\) | A1 | cao |
# Question 4:
## Part 4(a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(\uparrow)\ R = 5g - 14\sin30°$ | M1 A1 | M1: correct no. of terms, condone sin/cos confusion and sign errors. A1: correct equation in $R$ only |
| $R = 42\ \text{(N)}$ | A1 | Correct value (seen or implied) |
| Max Friction $= \frac{3}{7}\times42 = 18\ \text{(N)}$ | M1 | Use of $F=\frac{3}{7}R$ with their $R$ substituted. 18 only with no working cannot score this M mark |
| Horiz component of $P = 14\cos30° = 12.124\ldots$ and $12 < 18$ (their max friction). Must be comparing with **maximum** friction; 'maximum' must have been clearly stated somewhere. N.B. M0 if they state or imply friction **acting** on block is 18 N | M1 | Condone sin/cos confusion |
| Friction $= 12$ or better (N) and block doesn't move | A1 | cao and any equivalent correct statement and justification |
## Part 4(b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(\uparrow)\ P\sin30° + S = 5g$ | M1A1 | M1: correct no. of terms, condone sin/cos confusion and sign errors. A1: correct equation |
| $(\rightarrow)\ P\cos30° = \frac{3}{7}S$ (Allow M1A0 if they use max friction from (a), or $\frac{3}{7}\times\text{wrong value for }S$, allow M1A0 for $P\cos30°=F$) | M1A1 | M1: correct no. of terms, condone sin/cos confusion and sign errors. A1: correct equation |
| Solve for $P$ | DM1 | Dependent on both M marks; must be solving two equations in $P$ and one other unknown |
| $P = 19$ or $19.4\ \text{(N)}$ | A1 | cao |4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{61cb5bce-2fad-48f0-b6a4-e9899aa0acec-10_209_1017_255_466}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
A small block of mass 5 kg lies at rest on a rough horizontal plane.\\
The coefficient of friction between the block and the plane is $\frac { 3 } { 7 }$\\
A force of magnitude $P$ newtons is applied to the block in a direction which makes an angle of $30 ^ { \circ }$ with the plane, as shown in Figure 1.
The block is modelled as a particle.\\
Given that $P = 14$
\begin{enumerate}[label=(\alph*)]
\item find the magnitude of the frictional force exerted on the block by the plane and describe what happens to the block, justifying your answer.\\
(6)
The value of $P$ is now changed so that the block is on the point of slipping along the plane.
\item Find the value of $P$
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2022 Q4 [12]}}