A 1 kg block subjected to two simultaneous forces (2i + 3j + 4k) N and (3i - j - 2k) N is moved a distance of 25 m along (3i - 4j) direction. The work done in this process is ______ J. Numerical answer type. Work it out, then open the answer.

Answer: 35. Net force F = (2+3)i + (3-1)j + (4-2)k = 5i + 2j + 2k N Unit vector along 3i - 4j is (3i - 4j)/(5), so s = 25 · (3i - 4j)/(5) = 15i - 20j m W = 5(15) + 2(-20) + 2(0) = 75 - 40 = 35 J Work done = 35 J.

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Work by a Constant Force

A 1 kg block subjected to two simultaneous forces $(2\hat{i} + 3\hat{j} + 4\hat{k})\text{ N}$ and $(3\hat{i} - \hat{j} - 2\hat{k})\text{ N}$ is moved a distance of 25 m along $(3\hat{i} - 4\hat{j})$ direction. The work done in this process is ______ J.

Numerical answer type. Work it out, then open the answer.

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Answer: 35

Net force $\vec{F} = (2+3)\hat{i} + (3-1)\hat{j} + (4-2)\hat{k} = 5\hat{i} + 2\hat{j} + 2\hat{k}$ N
Unit vector along $3\hat{i} - 4\hat{j}$ is $\frac{3\hat{i} - 4\hat{j}}{5}$ , so $\vec{s} = 25 \cdot \frac{3\hat{i} - 4\hat{j}}{5} = 15\hat{i} - 20\hat{j}$ m
$W = 5(15) + 2(-20) + 2(0) = 75 - 40 = 35$ J
Work done $= 35$ J.

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