| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2003 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Vertically connected particles, air resistance |
| Difficulty | Standard +0.3 This is a standard two-particle connected system problem requiring straightforward application of Newton's second law. Part (i) involves simple equilibrium (statics), and part (ii) requires treating the connected particles as a system then finding internal tension—both are routine M1 techniques with no conceptual surprises or complex problem-solving. |
| Spec | 3.03b Newton's first law: equilibrium3.03c Newton's second law: F=ma one dimension3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| For resolving forces on any two of \(A\), or \(B\), or \(A\) and \(B\) combined \((T_1 = W_A + T_2, T_2 = W_B, T_1 = W_A + W_B)\) | M1 | |
| Tension in \(S_1\) is 4 N or Tension in \(S_2\) is 2 N | B1 | Accept 0.4\(g\) or 3.92 (from 9.8 or 9.81) for \(T_1\) |
| Tension in \(S_2\) is 2 N or Tension in \(S_1\) is 4 N | A1 | Accept 0.2\(g\) or 1.96 (from 9.8 or 9.81) for \(T_2\) |
| Answer | Marks | Guidance |
|---|---|---|
| For applying Newton's second law to \(A\), or to \(B\), or to \(A\) and \(B\) combined | M1 | |
| For any one of the equations \(T + 2 - 0.4 = 0.2a\), \(2 - T - 0.2 = 0.2a\), \(4 - 0.4 - 0.2 = 0.4a\) | A1 | |
| For a second of the above equations | A1 | |
| For solving the simultaneous equations for \(a\) and \(T\) | M1 | |
| Acceleration is 8.5 ms\(^{-2}\), tension is 0.1 N | A1 | Accept 8.3 from 9.8 or 8.31 from 9.81 |
| Answer | Marks |
|---|---|
| For applying Newton's second law to \(A\) and \(B\) combined | M1 |
| For \(4 - 0.4 - 0.2 = 0.4a\) | A1 |
| Acceleration is 8.5 ms\(^{-2}\) | A1 |
# Question 5:
## Part (i)
| For resolving forces on any two of $A$, or $B$, or $A$ and $B$ combined $(T_1 = W_A + T_2, T_2 = W_B, T_1 = W_A + W_B)$ | M1 | |
| Tension in $S_1$ is 4 N or Tension in $S_2$ is 2 N | B1 | Accept 0.4$g$ or 3.92 (from 9.8 or 9.81) for $T_1$ |
| Tension in $S_2$ is 2 N or Tension in $S_1$ is 4 N | A1 | Accept 0.2$g$ or 1.96 (from 9.8 or 9.81) for $T_2$ |
**SR** (for candidates who omit $g$) (Max 1 out of 3):
$T_1 = 0.4$ and $T_2 = 0.2$ B1
## Part (ii)
| For applying Newton's second law to $A$, or to $B$, or to $A$ and $B$ combined | M1 | |
| For any one of the equations $T + 2 - 0.4 = 0.2a$, $2 - T - 0.2 = 0.2a$, $4 - 0.4 - 0.2 = 0.4a$ | A1 | |
| For a second of the above equations | A1 | |
| For solving the simultaneous equations for $a$ and $T$ | M1 | |
| Acceleration is 8.5 ms$^{-2}$, tension is 0.1 N | A1 | Accept 8.3 from 9.8 or 8.31 from 9.81 |
**SR** (for candidates who obtain only the 'combined' equation) (Max 3 out of 5):
| For applying Newton's second law to $A$ and $B$ combined | M1 | |
| For $4 - 0.4 - 0.2 = 0.4a$ | A1 | |
| Acceleration is 8.5 ms$^{-2}$ | A1 | |
---5\\
\includegraphics[max width=\textwidth, alt={}, center]{cb04a09c-af23-4e9d-b3da-da9e351fe879-3_504_387_598_881}\\
$S _ { 1 }$ and $S _ { 2 }$ are light inextensible strings, and $A$ and $B$ are particles each of mass 0.2 kg . Particle $A$ is suspended from a fixed point $O$ by the string $S _ { 1 }$, and particle $B$ is suspended from $A$ by the string $S _ { 2 }$. The particles hang in equilibrium as shown in the diagram.\\
(i) Find the tensions in $S _ { 1 }$ and $S _ { 2 }$.
The string $S _ { 1 }$ is cut and the particles fall. The air resistance acting on $A$ is 0.4 N and the air resistance acting on $B$ is 0.2 N .\\
(ii) Find the acceleration of the particles and the tension in $S _ { 2 }$.
\hfill \mbox{\textit{CAIE M1 2003 Q5 [8]}}