# Question 7:

## Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| Continuous string; smooth ring | E1 | One reason |
| Light string | E1 | Another reason |

## Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Resolve $\leftarrow$: $60\cos\alpha - 60\cos\beta = 0$ | M1 | Resolution and an equation or equivalent. Accept $s\leftrightarrow c$. Accept a correct equation without method stated. Accept use of $T$ instead of 60 |
| so $\cos\alpha = \cos\beta$ and so $\alpha = \beta$ | E1 | Shown. Must have stated method (allow $\rightarrow$ seen) |

## Part (iii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Resolve $\uparrow$: $2\times60\times\sin\alpha - 8g = 0$ | M1 | Resolution and an equation. Accept $s\leftrightarrow c$. Do not award for resolution that cannot give solution (e.g. horizontal) |
| | B1 | Both strings used (accept use of half weight), seen in an equation |
| | B1 | $\sin\alpha$ or equivalent seen in an equation |
| so $\alpha = 40.7933\ldots$ so $40.8°$ (3 s.f.) | A1, A1 | All correct |

## Part (iv)
| Answer | Mark | Guidance |
|--------|------|----------|
| Resolve $\rightarrow$: $10 + T_{QC}\cos25 - T_{PC}\cos45 = 0$ | M1 | Recognise strings have different tensions |
| | M1 | Resolution and an equation. Accept $s\leftrightarrow c$. No extra forces. All forces present. Allow sign errors |
| | A1 | Correct. Any form |
| Resolve $\uparrow$: $T_{PC}\sin45 + T_{QC}\sin25 - 8g = 0$ | M1 | Resolution and an equation. Accept $s\leftrightarrow c$. No extra forces. All forces present. Allow sign errors |
| | A1 | Correct. Any form |
| Solving | M1 | A method that leads to at least one solution of a pair of simultaneous equations |
| $T_{CQ} = 51.4701\ldots$ so 51.5 N (3 s.f.) | A1 | cao either tension |
| $T_{CP} = 80.1120\ldots$ so 80.1 N (3 s.f.) | F1 | Other tension. Allow FT only if M1* awarded. Scale drawing: 1st M1 then A1, A1 for answers correct to 2 s.f. |

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