# Question 11:

## Part (a):

| Answer | Marks | Guidance |
|--------|-------|----------|
| $T_1 - 4.5 = 0.6(3.5)$ | M1 | 3.3 - N2L for $P$; correct number of terms and dimensionally consistent; allow sign confusion |
| $T_1 = 6.6$ (N) | A1 | 1.1 |

**Total: [2]**

## Part (b):

| Answer | Marks | Guidance |
|--------|-------|----------|
| For $Q$: $T_2 + 0.4g - T_1 = 0.4(3.5)$ | M1 | 3.3 - M1 for N2L for $Q$; correct number of terms and dimensionally consistent; allow sign confusion. Must be using $a=3.5$ |
| For $R$: $mg - T_2 = m(3.5)$ | M1 | 3.3 - M1 for N2L for $R$; correct number of terms. Or (by considering $Q$ and $R$ together): $(0.4+m)g - T_1 = (0.4+m)\times 3.5$ scores M2 A1 |
| Both correct (allow with their tension from (a)) | A1 | 1.1 |
| $m = 0.648$ | A1 | 1.1 - 3sf required $(0.6476190\ldots)$; $\left(m = \frac{68}{105}\right)$ |

**Total: [4]**

## Part (c):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Before string breaks $P$ moves $0.5(3.5)(0.4)^2\,(=0.28)$ | B1 | 3.4 - Correct (unsimplified) expression |
| When string breaks the speed of $P$ is $3.5(0.4)\,(=1.4)$ | B1 | 3.4 - Correct (unsimplified) expression |
| For $P$: $T - 4.5 = 0.6a$; For $Q$: $0.4g - T = 0.4a$ | M1* | 3.3 - M1 for attempt at N2L for both P and Q after string breaks; correct number of terms and dimensionally consistent but allow sign confusion. For reference if solved correctly then $a$ is $-0.58$ |
| Both equations correct | A1 | 1.1 |
| When string breaks $P$ travels a distance $s$ where $0 = 1.4^2 + 2(-0.58)s$ | M1dep* | 3.1b - Use of $v^2 = u^2 + 2as$ with $v=0$ and their values for $u$ and $a$. M0 if $a=3.5$ used. For reference $s = \frac{49}{29} = 1.689655\ldots$ |
| Total distance is $0.28 + 1.689\ldots = 1.9696\ldots < 2$ so $P$ does not reach the pulley | A1 | 2.2a - AG |

**Total: [6]**

## Part (d):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Both $P$ and the pulley are modelled as having negligible size rather than as objects with dimensions and therefore this could account for why $P$ does reach the pulley | B1 | 3.5a - An answer that refers to the dimensions of $P$ and/or the pulley. If more than one factor given then B1 if all are acceptable, B0 if not. Identifying a relevant factor is sufficient |

**Total: [1]**

## Question 11(d) — Appendix: Exemplar Responses

| Response | Mark | Guidance |
|---|---|---|
| Frictional force may not be constant | **B1** | Awarded |
| String not light | **B1** | Awarded |
| String not inextensible | **B1** | Awarded |
| String may be elastic | **B1** | Awarded |
| Elasticity | **B1** | Awarded |
| String may be extensible | **B1** | Awarded |
| Friction is constant | **B1** | Awarded |
| Friction (as a one word answer) | **B1** | Awarded |
| Surface being smooth | **B0** | Not awarded |
| Air resistance | **B0** | Not awarded |
| Particle may be smooth | **B0** | Not awarded |
| Frictional force on pulley | **B0** | Not awarded |