Mathematics 9709 · AS & A Level · Newton's laws of motion

Newton's laws of motion — practice question

Particles $A$ and $B$, with masses $0.8\,\text{kg}$ and $0.2\,\text{kg}$ respectively, are joined by a light inextensible string. $A$ rests on a horizontal plane. The string runs over a small smooth pulley $P$ at the edge of the plane, and $B$ is suspended freely. The horizontal part of the string, $AP$, has length $2.5\,\text{m}$. The particles are let go from rest, with both parts of the string taut.
(i)[5]

Assuming the surface is smooth, determine the time taken for $A$ to reach the pulley.

(ii)[5]

Now suppose the surface is rough and the coefficient of friction between $A$ and the surface is $0.1$; determine the speed of $A$ immediately before it reaches the pulley.

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