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\includegraphics[max width=\textwidth, alt={}, center]{ae5d1e27-5853-48aa-9046-86ce1c1a154a-5_488_739_269_703} One end of a light inextensible string is attached to a block of mass 1.5 kg . The other end of the string is attached to an object of mass 1.2 kg . The block is held at rest in contact with a rough plane inclined at \(21 ^ { \circ }\) to the horizontal. The string is taut and passes over a small smooth pulley at the bottom edge of the plane. The part of the string above the pulley is parallel to a line of greatest slope of the plane and the object hangs freely below the pulley (see diagram). The block is released and the object moves vertically downwards with acceleration \(\mathrm { am } \mathrm { s } ^ { - 2 }\). The tension in the string is TN . The coefficient of friction between the block and the plane is 0.8 .

1. Show that the frictional force acting on the block has magnitude 10.98 N , correct to 2 decimal places.
2. By applying Newton's second law to the block and to the object, find a pair of simultaneous equations in T and a .
3. Hence show that \(\mathrm { a } = 2.24\), correct to 2 decimal places.
4. Given that the object is initially 2 m above a horizontal floor and that the block is 2.8 m from the pulley, find the speed of the block at the instant when
   (a) the object reaches the floor,
   (b) the block reaches the pulley. \href{http://physicsandmathstutor.com}{physicsandmathstutor.com}
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