A body constrained to move along the y-axis i | vedclass

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(B) The force acting on the body is given by $\vec{F} = -\hat{i} + 2\hat{j} + 3\hat{k} \, 	ext{N}$.Since the body is constrained to move along the $y

Vedclass · Accepted Answer

$8$

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(B) The force acting on the body is given by $\vec{F} = -\hat{i} + 2\hat{j} + 3\hat{k} \, 	ext{N}$.Since the body is constrained to move along the $y$-axis for a distance of $4 \, 	ext{m}$,the displacement vector is $\vec{d} = 4\hat{j} \, 	ext{m}$.The work done $W$ by a constant force is defined as the dot product of the force vector and the displacement vector: $W = \vec{F} \cdot \vec{d}$.Substituting the given values: $W = (-\hat{i} + 2\hat{j} + 3\hat{k}) \cdot (4\hat{j})$.Using the properties of unit vectors ($\hat{i} \cdot \hat{j} = 0$,$\hat{j} \cdot \hat{j} = 1$,$\hat{k} \cdot \hat{j} = 0$),we get: $W = (-1)(0) + (2)(4) + (3)(0) = 8 \, 	ext{J}$.

$A$ body constrained to move along the $y$-axis is subjected to a constant force $\vec{F} = -\hat{i} + 2\hat{j} + 3\hat{k} \, \text{N}$. The work done by this force in moving the body a distance of $4 \, \text{m}$ along the $y$-axis is ............... $\text{J}$.

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