A body constrained to move along the z-axis o | vedclass

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(D) The force acting on the body is given by $F = -\hat{i} + 2\hat{j} + 3\hat{k} 	ext{ N}$.The displacement of the body is along the $z$-axis for a d

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(D) The force acting on the body is given by $F = -\hat{i} + 2\hat{j} + 3\hat{k} 	ext{ N}$.The displacement of the body is along the $z$-axis for a distance of $4 	ext{ m}$,so the displacement vector is $s = 4\hat{k} 	ext{ m}$.Work done $(W)$ is defined as the dot product of force and displacement: $W = F \cdot s$.$W = (-\hat{i} + 2\hat{j} + 3\hat{k}) \cdot (4\hat{k})$.Using the properties of unit vectors $(\hat{i} \cdot \hat{k} = 0, \hat{j} \cdot \hat{k} = 0, \hat{k} \cdot \hat{k} = 1)$:$W = (-1 	imes 0) + (2 	imes 0) + (3 	imes 4) = 0 + 0 + 12 = 12 	ext{ J}$.Therefore,the work done by the force is $12 	ext{ J}$.

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