| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Particle on rod or wire with friction |
| Difficulty | Standard +0.3 This is a standard friction equilibrium problem requiring resolution of forces, application of F≤μR, and then a straightforward F=ma calculation. The two-part structure and use of limiting friction are typical for M1, but the problem follows a well-established template with no novel insight required—slightly easier than average due to straightforward geometry and clear problem structure. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces |
| Answer | Marks |
|---|---|
| 4 | Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw). |
| Answer | Marks | Guidance |
|---|---|---|
| 4(a) | Resolving forces in either direction | M1 |
| R = T sin30 + 0.1g, F = T cos30 | A1 | |
| T cos30 = 0.8 (T sin30 + 0.1g) | M1 | |
| T = 1.72 (1.7166...) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 4(b) | R = 3sin30 + 0.1g | B1 |
| 3 cos30 – 0.8(3sin30 + 0.1g) = 0.1a | M1 | |
| a = 5.98 ms–2 (5.9807...) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 4:
4 | Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw).
--- 4(a) ---
4(a) | Resolving forces in either direction | M1
R = T sin30 + 0.1g, F = T cos30 | A1
T cos30 = 0.8 (T sin30 + 0.1g) | M1
T = 1.72 (1.7166...) | A1
4
--- 4(b) ---
4(b) | R = 3sin30 + 0.1g | B1
3 cos30 – 0.8(3sin30 + 0.1g) = 0.1a | M1
a = 5.98 ms–2 (5.9807...) | A1
3
Question | Answer | MarksThe diagram shows a ring of mass $0.1\text{ kg}$ threaded on a fixed horizontal rod. The rod is rough and the coefficient of friction between the ring and the rod is $0.8$. A force of magnitude $T\text{ N}$ acts on the ring in a direction at $30°$ to the rod, downwards in the vertical plane containing the rod. Initially the ring is at rest.
\includegraphics{figure_4}
\begin{enumerate}[label=(\alph*)]
\item Find the greatest value of $T$ for which the ring remains at rest. [4]
\item Find the acceleration of the ring when $T = 3$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2020 Q4 [7]}}