A force of 4 N has the direction π/3. What is the work done in moving an object from the point (1, 2) to the point (5, 4), where distances are measured in meters?

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A unit vector with direction [latex]\pi / 3[/latex] is given by [latex]\mathbf{u}=(\cos \pi / 3) \mathbf{i}+(\sin \pi / 3) \mathbf{j}=(1 / 2) \mathbf{i}+(\sqrt{3} / 2) \mathbf{j}[/latex]. Thus [latex]\mathbf{F}=4 \mathbf{u}=2 \mathbf{i}+2 \sqrt{3} \mathbf{j}[/latex]. The displacement vector [latex]\mathbf{d}[/latex] is given by [latex](5-1) \mathbf{i}+(4-2) \mathbf{j}=4 \mathbf{i}+2 \mathbf{j}[/latex]. Thus

[latex]W=\mathbf{F} \cdot \mathbf{d}=(2 \mathbf{i}+2 \sqrt{3} \mathbf{j}) \cdot(4 \mathbf{i}+2 \mathbf{j})=(8+4 \sqrt{3}) \approx 14.93 \mathrm{~N} \cdot \mathrm{m}[/latex]

The component of [latex]\mathbf{F}[/latex] in the direction of motion is sketched in Figure 5 .

Question 3.4: A force of 4 N has the direction π/3. What is the work done ...

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