| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| 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 two-part mechanics problem requiring resolution of forces and application of the limiting friction formula F = μR. Part (i) involves simple vertical equilibrium (R = 7g - X cos 15°), and part (ii) requires horizontal equilibrium with F = μR. Both are standard textbook exercises with no problem-solving insight needed, making it easier than average but not trivial due to the angled force component. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03u Static equilibrium: on rough surfaces |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(N + \text{component of } X = \text{Weight of } B\) | M1 | For resolving forces acting on the block vertically (3 terms required) |
| Normal component is \((70 - X\cos15°)\) N | A1 [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(F = X\sin15°\) | B1 | |
| \(X\sin15° = 0.4(70 - X\cos15°)\) | M1 | For using \(F = \mu R\) |
| Value of \(X\) is \(43.4\) | A1 [3] |
## Question 1:
### Part (i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $N + \text{component of } X = \text{Weight of } B$ | M1 | For resolving forces acting on the block vertically (3 terms required) |
| Normal component is $(70 - X\cos15°)$ N | A1 [2] | |
### Part (ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $F = X\sin15°$ | B1 | |
| $X\sin15° = 0.4(70 - X\cos15°)$ | M1 | For using $F = \mu R$ |
| Value of $X$ is $43.4$ | A1 [3] | |
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\includegraphics[max width=\textwidth, alt={}, center]{139371b7-e142-4ed6-bff3-3ca4c32b9c6b-2_426_424_258_863}
A block $B$ of mass 7 kg is at rest on rough horizontal ground. A force of magnitude $X \mathrm {~N}$ acts on $B$ at an angle of $15 ^ { \circ }$ to the upward vertical (see diagram).\\
(i) Given that $B$ is in equilibrium find, in terms of $X$, the normal component of the force exerted on $B$ by the ground.\\
(ii) The coefficient of friction between $B$ and the ground is 0.4 . Find the value of $X$ for which $B$ is in limiting equilibrium.
\hfill \mbox{\textit{CAIE M1 2014 Q1 [5]}}