5 One end of a light elastic string of natural length 0.4 m and modulus of elasticity 16 N is attached to a fixed point \(O\) of a horizontal table. A particle \(P\) of mass 0.8 kg is attached to the other end of the string. The particle \(P\) is released from rest on the table, at a point which is 0.5 m from \(O\). The coefficient of friction between the particle and the table is 0.2 . By considering work and energy, find the speed of \(P\) at the instant the string becomes slack.

Loss in EPE = $\frac{16(0.1)^2}{2 \times 0.4}$ | B1 | ($= 0.2$)
For using $F = \mu R$ and $R = mg$ | M1 |
$F = 0.2 \times 0.8 \times 10$ | A1 | ($=1.6$)
WD against friction = $1.6 \times 0.1$ | B1 ft | ($= 0.16$)
For using KE gained = EPE lost – WD against friction | M1 |
$\frac{1}{2}0.8v^2 = 0.2 - 0.16$ | A1 ft |
Speed is 0.316 ms$^{-1}$ | A1 | 7 marks

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5 One end of a light elastic string of natural length 0.4 m and modulus of elasticity 16 N is attached to a fixed point $O$ of a horizontal table. A particle $P$ of mass 0.8 kg is attached to the other end of the string. The particle $P$ is released from rest on the table, at a point which is 0.5 m from $O$. The coefficient of friction between the particle and the table is 0.2 . By considering work and energy, find the speed of $P$ at the instant the string becomes slack.

\hfill \mbox{\textit{CAIE M2 2004 Q5 [7]}}