## Question 4:

**Part (i):**

| Answer | Mark | Guidance |
|--------|------|----------|
| Any one force in correct direction correctly labelled with arrow **or** all forces with correct directions and arrows | B1 | A force may be replaced by its components if labelled correctly e.g. $mg\cos20°$, $mg\sin20°$ |
| All correct (Accept words for labels and weight as $W$, $mg$, 147 (N)) No extra or duplicate forces | B1 | Do not allow force **and** its components unless components are clearly distinguished, e.g. by broken lines |
| **Total: 2** | | |

**Part (ii) — Either (Up the plane):**

| Answer | Mark | Guidance |
|--------|------|----------|
| $P\cos20 - 15 \times 9.8 \times \sin20 = 0$ | M1 | Attempt to resolve at least one force up plane. Accept mass not weight. No extra forces. If other directions used, all forces must be present but see below for resolving vertically and horizontally |
| | A1 | Accept only error as consistent $s \leftrightarrow c$ |
| $P = 53.50362\ldots$ so $53.5$ (3 s.f.) | A1 | cao |
| **Total: 3** | | |

**Or (Vertically and horizontally):**

| Answer | Mark | Guidance |
|--------|------|----------|
| $R\cos20° = 15g$, $R\sin20° = P$, Eliminate $R$ | M1 | Attempt to resolve all forces both horizontally and vertically and attempt to combine into a single equation. No extra forces. Accept $s \leftrightarrow c$. Accept mass not weight |
| $P = \dfrac{15g}{\cos20°} \times \sin20°$ | A1 | Accept only error as consistent $s \leftrightarrow c$ |
| $P = 53.5$ (3 s.f.) | A1 | cao |
| **Total: 3** | | |

**Or (Triangle of forces):**

| Answer | Mark | Guidance |
|--------|------|----------|
| Triangle drawn and labelled | M1 | All sides must be labelled and in correct orientation; three forces only; condone no arrows |
| $\dfrac{P}{15g} = \tan20°$ | A1 | Oe |
| $P = 53.5$ (3 s.f.) | A1 | cao |
| **Total: 3** | | |

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