# Question 8:

## Part (a):

| Answer/Working | Marks | Guidance |
|---|---|---|
| Extension when fallen $x$ m: $(x - 26)$ for $x \geq 26$ | | |
| EPE $= \frac{\lambda e^2}{2l} = \frac{1456(x-26)^2}{2 \times 26}$ | M1 | Correct EPE formula with correct values |
| Energy conservation: $\frac{1}{2}(70)v^2 = 70g(x) - \frac{1456(x-26)^2}{52}$ | M1 A1 | Conservation of energy equation, correct terms |
| $35v^2 = 686x - 28(x-26)^2$ | | |
| $35v^2 = 686x - 28(x^2 - 52x + 676)$ | DM1 | Expanding and simplifying |
| $35v^2 = 686x - 28x^2 + 1456x - 18928$ | | |
| $5v^2 = 306x - 4x^2 - 2704$ | A1 | Shown correctly (QED) |

## Part (b):

| Answer/Working | Marks | Guidance |
|---|---|---|
| When $x < 26$ the cord is slack/not taut, so there is no elastic potential energy term | B1 | Must indicate cord not stretched |

## Part (c):

| Answer/Working | Marks | Guidance |
|---|---|---|
| Maximum $x$ when $v = 0$: $4x^2 - 306x + 2704 = 0$ | M1 | Setting $v = 0$ and solving |
| $x = \frac{306 \pm \sqrt{306^2 - 4(4)(2704)}}{8}$ | | |
| $x = 57.25$ or $x = 11.75$ (reject as $< 26$) | A1 | $x = 57.25$ m (accept 57.3) |

## Part (d)(i):

| Answer/Working | Marks | Guidance |
|---|---|---|
| Speed maximum when $\frac{dv}{dx} = 0$, i.e. $\frac{d(v^2)}{dx} = 0$ | M1 | Differentiating and setting equal to zero |
| $\frac{d(5v^2)}{dx} = 306 - 8x = 0 \Rightarrow x = 38.25$ m | A1 | |

## Part (d)(ii):

| Answer/Working | Marks | Guidance |
|---|---|---|
| $5v^2 = 306(38.25) - 4(38.25)^2 - 2704$ | M1 | Substituting $x = 38.25$ |
| $v = \sqrt{\frac{306(38.25)-4(38.25)^2-2704}{5}}$ | | |
| $v \approx 23.6$ m s$^{-1}$ | A1 | |

These pages appear to be blank answer spaces (pages 17-19 for Question 8, and pages 20-21 for Question 9) from an AQA Mechanics paper (P/Jun15/MM2B). They do not contain any mark scheme content - they are the student answer booklet pages.

To obtain the mark scheme for this paper, I would recommend:

- Searching **AQA's website** (aqa.org.uk) for the June 2015 MM2B mark scheme
- Checking **Physics & Maths Tutor** (physicsandmathstutor.com) which hosts past paper mark schemes

The question text visible for **Question 9** involves a rod PQ of length $2a$ resting on rough ground at P and a semicircular prism at T, inclined at $30°$, with coefficient of friction $\mu$ at both contact points, but the mark scheme itself is not shown in these images.

These pages (22, 23, and 24) are **answer/working space pages** from an AQA exam paper (P/Jun15/MM2B). They contain:

- Blank lined answer spaces for **Question 9**
- A final blank page stating "There are no questions printed on this page"

**There is no mark scheme content on these pages.** These are student answer booklet pages, not mark scheme pages. No questions, answers, mark allocations, or guidance notes are printed here.

To obtain the mark scheme for this paper (AQA MM2B June 2015), you would need to access it directly from the **AQA website** or **PMT (Physics & Maths Tutor)** mark scheme documents.