Consider a particle on which constant forces | vedclass

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(A) Given:$F_{1} = (\hat{i} + 2\hat{j} + 3\hat{k}) 	ext{ N}$$F_{2} = (4\hat{i} - 5\hat{j} - 2\hat{k}) 	ext{ N}$$r_{1} = (20\hat{i} + 15\hat{j}) 	ex

Vedclass · Accepted Answer

$-0.48 	ext{ J}$

Vedclass · Answer

(A) Given:$F_{1} = (\hat{i} + 2\hat{j} + 3\hat{k}) 	ext{ N}$$F_{2} = (4\hat{i} - 5\hat{j} - 2\hat{k}) 	ext{ N}$$r_{1} = (20\hat{i} + 15\hat{j}) 	ext{ cm} = (0.2\hat{i} + 0.15\hat{j}) 	ext{ m}$$r_{2} = (7\hat{k}) 	ext{ cm} = (0.07\hat{k}) 	ext{ m}$Total force $F = F_{1} + F_{2} = (1+4)\hat{i} + (2-5)\hat{j} + (3-2)\hat{k} = (5\hat{i} - 3\hat{j} + \hat{k}) 	ext{ N}$.Displacement $s = r_{2} - r_{1} = (0\hat{i} + 0\hat{j} + 0.07\hat{k}) - (0.2\hat{i} + 0.15\hat{j} + 0\hat{k}) = (-0.2\hat{i} - 0.15\hat{j} + 0.07\hat{k}) 	ext{ m}$.Work done $W = F \cdot s = (5\hat{i} - 3\hat{j} + \hat{k}) \cdot (-0.2\hat{i} - 0.15\hat{j} + 0.07\hat{k})$.$W = (5 	imes -0.2) + (-3 	imes -0.15) + (1 	imes 0.07)$.$W = -1.0 + 0.45 + 0.07 = -0.48 	ext{ J}$.

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