| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Applied force in addition to weights |
| Difficulty | Standard +0.3 This is a standard A-level mechanics pulley problem with two parts: (a) requires setting up Newton's second law equations for connected particles with an applied force, solving simultaneous equations for tension and acceleration; (b) uses work-energy methods with friction. While it involves multiple concepts (pulleys, inclined planes, friction, energy), these are routine M1 techniques with straightforward application and no novel insight required. Slightly easier than average due to clear setup and standard methods. |
| Spec | 3.03l Newton's third law: extend to situations requiring force resolution3.03o Advanced connected particles: and pulleys6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| For \(A\): \(T = 0.3a\); For \(B\): \(3.5 + 0.5g\sin 30° - T = 0.5a\); System: \(3.5 + 0.5g\sin 30° = (0.3 + 0.5)a\) | M1 | For applying Newton's 2nd law for either particle \(A\) or particle \(B\) or to the system. Correct number of terms. |
| Two correct equations | A1 | |
| For solving either for \(T\) or for \(a\) | M1 | |
| \(a = 7.5\ \text{ms}^{-2}\) | A1 | |
| \(T = 2.25\ \text{N}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(0.5g\sin 30° \times 0.6\ [= 1.5]\) | B1 | PE loss by \(B\) |
| Apply the work-energy equation to the system | M1 | 5 relevant terms, their PE for \(0.5\) kg, WD by \(3.5\) N, WD against friction and two relevant KE terms |
| \(0.5g\sin 30° \times 0.6 + 3.5 \times 0.6 = \frac{1}{2} \times 0.8 \times v^2 + 1.1\) | A1 | |
| \(v = 2.5\ \text{ms}^{-1}\) | A1 |
## Question 8(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| For $A$: $T = 0.3a$; For $B$: $3.5 + 0.5g\sin 30° - T = 0.5a$; System: $3.5 + 0.5g\sin 30° = (0.3 + 0.5)a$ | M1 | For applying Newton's 2nd law for either particle $A$ or particle $B$ or to the system. Correct number of terms. |
| Two correct equations | A1 | |
| For solving either for $T$ or for $a$ | M1 | |
| $a = 7.5\ \text{ms}^{-2}$ | A1 | |
| $T = 2.25\ \text{N}$ | A1 | |
---
## Question 8(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $0.5g\sin 30° \times 0.6\ [= 1.5]$ | B1 | PE loss by $B$ |
| Apply the work-energy equation to the system | M1 | 5 relevant terms, their PE for $0.5$ kg, WD by $3.5$ N, WD against friction and two relevant KE terms |
| $0.5g\sin 30° \times 0.6 + 3.5 \times 0.6 = \frac{1}{2} \times 0.8 \times v^2 + 1.1$ | A1 | |
| $v = 2.5\ \text{ms}^{-1}$ | A1 | |8\\
\includegraphics[max width=\textwidth, alt={}, center]{fcc3d739-5c36-48ad-9c34-f69b28a06dba-14_388_1216_264_461}
Two particles $A$ and $B$, of masses 0.3 kg and 0.5 kg respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to a horizontal plane and to the top of an inclined plane. The particles are initially at rest with $A$ on the horizontal plane and $B$ on the inclined plane, which makes an angle of $30 ^ { \circ }$ with the horizontal. The string is taut and $B$ can move on a line of greatest slope of the inclined plane. A force of magnitude 3.5 N is applied to $B$ acting down the plane (see diagram).
\begin{enumerate}[label=(\alph*)]
\item Given that both planes are smooth, find the tension in the string and the acceleration of $B$.
\item It is given instead that the two planes are rough. When each particle has moved a distance of 0.6 m from rest, the total amount of work done against friction is 1.1 J .
Use an energy method to find the speed of $B$ when it has moved this distance down the plane. [You should assume that the string is sufficiently long so that $A$ does not hit the pulley when it moves 0.6 m .]\\
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2020 Q8 [9]}}