A block slides on a horizontal table

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

A 4 kg4\,\text{kg} block slides on a horizontal table. Two constant forces act simultaneously on the block while it undergoes a displacement given by s=(3ı^+4ȷ^) m\mathbf{s} = (3\hat\imath + 4\hat\jmath)\,\text{m}. The forces are F1=(12ı^+5ȷ^) N\mathbf{F}_1 = (12\hat\imath + 5\hat\jmath)\,\text{N} and a kinetic friction force F2=(−8ı^) N\mathbf{F}_2 = (-8\hat\imath)\,\text{N}. (i) Draw and label the two forces and the displacement on a set of mutually perpendicular xx and yy axes. (ii) Compute the net work done on the block by the two forces during the given displacement. (iii) If the block was initially moving with a speed of 2 m s−12\,\text{m}\,\text{s}^{-1}, determine its final speed after the displacement. (iv) Calculate the angle between the net force and the displacement. If the block had instead moved through the same magnitude of displacement but exactly along the direction of the net force, state whether the net work would be greater, smaller or the same. Justify your answer quantitatively.

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