Exercise · ZW-VECTOR-LINE-INTEGRAL-005 · ★☆☆ Basic
A constant force \(\mathbf F=\langle2,3\rangle\) moves a particle in a straight line from \((0,0)\) to \((4,1)\). How much work does it do?
Choose one option.
Show answer
- C. \(11\)
Explanation
With a constant force, work is \(\mathbf F\cdot\Delta\mathbf r=2\cdot4+3\cdot1=11\). The value \(14\) comes from multiplying the crossed components.
Review the concept: Line integral of a vector field
The line integral of a vector field \(\mathbf F\) over an oriented curve \(C\), parametrized by \(\mathbf r(t)\), \(a\le t\le b\), measures the work \(\mathbf F\) does along \(C\).
\[\int_C \mathbf F\cdot d\mathbf r=\int_a^b \mathbf F(\mathbf r(t))\cdot\mathbf r'(t)\,dt\]
More practice problems: line integral of a vector field
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