A particle $$\(A\)$$ of mass $$\(4 \mathrm{~kg}\)$$ is held at rest on a rough horizontal table. Particle $$\(A\)$$ is attached to one end of a string that passes over a pulley $$\(P\)$$. The pulley is fixed at the edge of the table. The other end of the string is attached to a particle $$\(B\)$$, of mass $$\(3 \mathrm{~kg}\)$$, which hangs freely below $$\(P\)$$. The part of the string from $$\(A\)$$ to $$\(P\)$$ is perpendicular to the edge of the table and $$\(A, P\)$$ and $$\(B\)$$ all lie in the same vertical plane. The string is modelled as being light and inextensible and the pulley is modelled as being small, smooth and light. The system is released from rest with the string taut. At the instant of release, $$\(A\)$$ is $$\(2 \mathrm{~m}\)$$ from the edge of the table and $$\(B\)$$ is $$\(1.4 \mathrm{~m}\)$$ above a horizontal floor, as shown in Figure 3. After descending with constant acceleration for 2 seconds, $$\(B\)$$ hits the floor and does not rebound. (a) Show that the acceleration of $$\(A\)$$ before $$\(B\)$$ hits the floor is $$\(0.7 \mathrm{~m} \mathrm{~s}^{-2}\)$$ (2) (b) State which of the modelling assumptions you have used in order to answer part (a). (1) (c) Find the magnitude of the resultant force exerted on the pulley by the string. (4) The coefficient of friction between $$\(A\)$$ and the table is $$\(\mu\)$$. (d) Find the value of $$\(\mu\)$$. (6) (e) Determine, by calculation, whether or not $$\(A\)$$ reaches the pulley. (5)

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