First slide

Work

Question

Consider a force $\vec{F} = - x \hat{i} + y \hat{j}$ . The work done by this force in moving a particle from point $A (1, 0)$ to $B (0, 1)$ along the line segment is (all quantities are in SI units)

Moderate

A

$\frac{1}{2}$
B

$\frac{3}{2}$
C

1
D

2

Solution

$\begin{array}{l} L e t \vec{d s} = d x \hat{i} + d y \hat{j} + d z \hat{k} \\ T h e n, w o r k d o n e = d w = \vec{F} . \vec{d s} \\ \Rightarrow W = \int^{} (- x \hat{i} + y \hat{j}) . (d x \hat{i} + d y \hat{j} + d z \hat{k}) \\ \Rightarrow W = \int^{} (- x d x + y d y) \\ \Rightarrow W = -_{1}^{0} x d x +_{0}^{1} y d y \\ \Rightarrow W = - (0 - \frac{1}{2}) + (\frac{1}{2} - 0) = 1 J \end{array}$

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