| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | String at angle to slope |
| Difficulty | Standard +0.3 This is a standard inclined plane mechanics problem requiring resolution of forces in two directions. Part (i) involves equilibrium conditions with straightforward trigonometry to find an angle, while part (ii) applies F=ma with given angle. The problem is slightly easier than average as it follows a routine template with clear setup and standard techniques, though it requires careful component resolution. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 3(i) | M1 | Attempt to resolve forces along the plane |
| Answer | Marks | Guidance |
|---|---|---|
| 100 cos θ = 8 g sin 30 → θ = 66.4 | A1 | |
| [R = 8 g cos 30 + 100 sin θ] | M1 | Resolve forces perpendicular to the plane |
| Answer | Marks |
|---|---|
| R = 161 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 3(ii) | 100 cos 30 – 8g sin 30 = 8a | M1 |
| Answer | Marks |
|---|---|
| a = 5.83 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 3:
--- 3(i) ---
3(i) | M1 | Attempt to resolve forces along the plane
(2 terms)
100 cos θ = 8 g sin 30 → θ = 66.4 | A1
[R = 8 g cos 30 + 100 sin θ] | M1 | Resolve forces perpendicular to the plane
(3 terms)
R = 161 | A1
4
--- 3(ii) ---
3(ii) | 100 cos 30 – 8g sin 30 = 8a | M1 | Apply Newton’s 2nd law parallel to the
plane (3 terms)
a = 5.83 | A1
2
Question | Answer | Marks | Guidance\includegraphics{figure_3}
A particle $P$ of mass $8 \text{ kg}$ is on a smooth plane inclined at an angle of $30°$ to the horizontal. A force of magnitude $100 \text{ N}$, making an angle of $\theta°$ with a line of greatest slope and lying in the vertical plane containing the line of greatest slope, acts on $P$ (see diagram).
\begin{enumerate}[label=(\roman*)]
\item Given that $P$ is in equilibrium, show that $\theta = 66.4$, correct to $1$ decimal place, and find the normal reaction between the plane and $P$. [4]
\item Given instead that $\theta = 30$, find the acceleration of $P$. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2018 Q3 [6]}}