| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Friction |
| Type | Single angled force - find limiting friction or coefficient |
| Difficulty | Moderate -0.8 This is a straightforward mechanics problem requiring resolution of forces in two directions and application of F=μR at limiting equilibrium. The setup is standard (single angled force, horizontal surface), requires only routine application of Newton's laws and friction formula, with no problem-solving insight needed beyond the basic method taught in M1. |
| Spec | 1.05g Exact trigonometric values: for standard angles3.03m Equilibrium: sum of resolved forces = 0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Diagram showing 4 forces: \(R\) (normal reaction), \(30\text{N}\) (applied force at \(24°\)), \(Fr\) (friction), \(4g\) (weight) | B1 | 4 forces, labelled |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| For resolving horizontally or vertically | M1 | |
| \(30\cos 24 = F\) \((F = 27.406...)\) | A1 | |
| \(R + 30\sin 24 = 40\) \((R = 27.797...)\) | A1 | |
| \(\mu = \dfrac{30\cos 24}{40 - 30\sin 24}\) | M1 | Using \(\mu = F/R\) |
| \(\mu = 0.986\) \((0.9859...)\) | A1 |
## Question 3(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Diagram showing 4 forces: $R$ (normal reaction), $30\text{N}$ (applied force at $24°$), $Fr$ (friction), $4g$ (weight) | B1 | 4 forces, labelled |
## Question 3(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| For resolving horizontally or vertically | M1 | |
| $30\cos 24 = F$ $(F = 27.406...)$ | A1 | |
| $R + 30\sin 24 = 40$ $(R = 27.797...)$ | A1 | |
| $\mu = \dfrac{30\cos 24}{40 - 30\sin 24}$ | M1 | Using $\mu = F/R$ |
| $\mu = 0.986$ $(0.9859...)$ | A1 | |3 A string is attached to a block of mass 4 kg which rests in limiting equilibrium on a rough horizontal table. The string makes an angle of $24 ^ { \circ }$ above the horizontal and the tension in the string is 30 N .
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram showing all the forces acting on the block.
\item Find the coefficient of friction between the block and the table.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2020 Q3 [6]}}