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

Newton's laws of motion — practice question

A particle with mass 12 kg is to be dragged over a rough horizontal surface by a light inextensible string. The string makes an angle of $30^\circ$ to the plane, and its tension is $T$ N (see diagram). The coefficient of friction between the particle and the plane is 0.5.
(a)[5]

As the particle is on the point of moving, find the value of $T$.

(b)[3]

If instead the particle is accelerating at $0.2\,\text{m s}^{-2}$, find the value of $T$.

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