First slide

Scalars and Vectors

Question

Two forces $F_{1} = (\hat{i} + j + \hat{k}) N and F_{2} = (\hat{i} + 2 \hat{j} + 3 \hat{k}) N$ act on a block and displace it from point A (2,3,4) m to the point B (5,4,3) m. Determine work done (in joule).

Moderate

Solution

The net work done,
$\begin{array}{l} W = {\vec{F}}_{1} \cdot \vec{s} + {\vec{F}}_{2} \cdot \vec{s} = ({\vec{F}}_{1} + {\vec{F}}_{2}) \cdot \vec{s} \\ = (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) \cdot (r_{B} - r_{A}) \\ = (2 \tilde{i} + 3 \tilde{j} + 4 \tilde{k}) \cdot {(5 \tilde{i} + 4 \tilde{j} + 3 \tilde{k}) - (2 \tilde{i} + 3 \tilde{j} + 4 \tilde{k})} . \\ = (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) \cdot (3 \hat{i} + \hat{j} - \hat{k}) = 6 + 3 - 4 = 5 J \end{array}$

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