3 \includegraphics[max width=\textwidth, alt={}, center]{3e7472a8-df1e-45c4-81fb-e4397bddf5ad-2_202_972_1619_584} A light elastic string has natural length 0.8 m and modulus of elasticity 12 N . The ends of the string are attached to fixed points \(A\) and \(B\), which are at the same horizontal level and 0.96 m apart. A particle of weight \(W \mathrm {~N}\) is attached to the mid-point of the string and hangs in equilibrium at a point 0.14 m below \(A B\) (see diagram). Find \(W\).

| Obtains extension of string as 0.2m (or half-extension as 0.1m) | B1 |
| Finds the tension by using the correct Hooke's Law formula $[T = 12 \times 0.2/0.8 \text{ or } T = 12 \times 0.1/0.4]$ | M1 |
| $T = 12 \times 0.2/0.8 \text{ or } T = 12 \times 0.1/0.4 \quad [= 3]$ | A1 |
| Resolves forces on the particle vertically and substitutes for $T$ $[W = 2 \times 3 \times (0.14/0.5) \text{ or } 2 \times 3 \cos 73.74°]$ | M1 |
| Obtains $W = 1.68$ | A1 | 5 marks |

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\includegraphics[max width=\textwidth, alt={}, center]{3e7472a8-df1e-45c4-81fb-e4397bddf5ad-2_202_972_1619_584}

A light elastic string has natural length 0.8 m and modulus of elasticity 12 N . The ends of the string are attached to fixed points $A$ and $B$, which are at the same horizontal level and 0.96 m apart. A particle of weight $W \mathrm {~N}$ is attached to the mid-point of the string and hangs in equilibrium at a point 0.14 m below $A B$ (see diagram). Find $W$.

\hfill \mbox{\textit{CAIE M2 2002 Q3 [5]}}