A particle travels from a position r _1 = (2 m) i + (3 m) j to a new position r _2 = (3 m) i + (2 m) j while experiencing a force F = (5 N) i + (5 N) j . Determine the work done by this force on the particle over the

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Quantrex Academy · Accepted Answer

Correct answer: D. 0 J

The displacement vector of the particle is given by:

\Delta\vec{r} = \vec{r}_2 - \vec{r}_1

\Delta\vec{r} = (3\hat{i} + 2\hat{j}) - (2\hat{i} + 3\hat{j})

\Delta\vec{r} = \hat{i} - \hat{j} \text{ m}

The work done by the constant force is the dot product of the force and the displacement:

W = \vec{F} \cdot \Delta\vec{r}

W = (5\hat{i} + 5\hat{j}) \cdot (\hat{i} - \hat{j})

W = (5)(1) + (5)(-1)

W = 5 - 5 = 0 \text{ J}

A particle travels from a position r _1 = (2 m) i + (3 m) j to a...

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