| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2017 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Motion on a slope |
| Type | Motion with applied force on slope |
| Difficulty | Moderate -0.8 This is a straightforward mechanics problem requiring standard resolution of forces on an inclined plane. Part (i) is a simple 'show that' calculation (mg sin 20°), and part (ii) applies F=ma with given friction coefficient—both are routine textbook exercises with no problem-solving insight required. |
| Spec | 3.03u Static equilibrium: on rough surfaces3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| 1(i) | F = 0.2g sin 20 = 0.684 N | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 1(ii) | R = 0.2g cos 20 | B1 |
| F = µR [= 0.6 × 0.2g cos 20] | M1 | Using F = µR F = 1.1276… |
| [0.9 + 0.2g sin 20 – F = 0.2a] | M1 | Use of Newton’s 2nd law along the plane |
| Answer | Marks |
|---|---|
| a = 2.28 ms-2 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 1:
--- 1(i) ---
1(i) | F = 0.2g sin 20 = 0.684 N | B1 | AG
1
--- 1(ii) ---
1(ii) | R = 0.2g cos 20 | B1
F = µR [= 0.6 × 0.2g cos 20] | M1 | Using F = µR F = 1.1276…
[0.9 + 0.2g sin 20 – F = 0.2a] | M1 | Use of Newton’s 2nd law along the plane
(4 relevant terms)
a = 2.28 ms-2 | A1
4
Question | Answer | Marks | GuidanceA particle of mass 0.2 kg is resting in equilibrium on a rough plane inclined at $20°$ to the horizontal.
\begin{enumerate}[label=(\roman*)]
\item Show that the friction force acting on the particle is 0.684 N, correct to 3 significant figures. [1]
\end{enumerate}
The coefficient of friction between the particle and the plane is 0.6. A force of magnitude 0.9 N is applied to the particle down a line of greatest slope of the plane. The particle accelerates down the plane.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find this acceleration. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2017 Q1 [5]}}