(a) For a particle simultaneously subjected to the constant forces ( F_1, F_2, , F_n…

PHYSICS · Subjective · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

(a) For a particle simultaneously subjected to the constant forces F⃗1,F⃗2,…,F⃗n\vec F_1,\vec F_2,\dots,\vec F_n and displaced by s⃗,\vec s, derive an expression showing that the total work done equals the dot product of the resultant force with the displacement. (b) Three forces act on a particle: F⃗1=7 ı^−4 ȷ^  N,  F⃗2=−3 ı^+6 ȷ^  N,  F⃗3=2 ı^+5 ȷ^  N.\vec F_1 = 7\,\hat\imath - 4\,\hat\jmath\;\text{N},\; \vec F_2 = -3\,\hat\imath + 6\,\hat\jmath\;\text{N},\; \vec F_3 = 2\,\hat\imath + 5\,\hat\jmath\;\text{N}. If the particle undergoes a displacement s⃗=5 ı^+2 ȷ^  m,\vec s = 5\,\hat\imath + 2\,\hat\jmath\;\text{m}, calculate: (i) the resultant force, (ii) the net work done. (c) If the mass of the particle is 2\,kg and it was initially at rest, find its speed after the displacement, assuming no other forces act.

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