First slide

Definition of Work

Question

A particle moves from a point $(- 2 \hat{i} + 5 \hat{j}) to (4 \hat{j} + 3 \hat{k})$ when a force of $(4 \hat{i} + 3 \hat{j})$ N is applied. How much work has been done by the force?

Easy

A

8 J
B

5 J
C

11 J
D

2 J

Solution

$\begin{array}{l} Here {\vec{r}}_{1} = (- 2 \hat{i} + 5 \hat{j}) m, {\vec{r}}_{2} = (4 \hat{j} + 3 \hat{k}) m \\ \vec{F} = (4 \hat{i} + 3 \hat{j}) N, W = ? \end{array}$
$Work done by force F in moving from {\vec{r}}_{1} to {\vec{r}}_{2},$
$W = \vec{F} \cdot ({\vec{r}}_{2} - {\vec{r}}_{1})$
$W = (4 \hat{i} + 3 \hat{j}) \cdot (4 \hat{j} + 3 \hat{k} + 2 \hat{i} - 5 \hat{j})$
$= (4 \hat{i} + 3 \hat{j}) \cdot (2 \hat{i} - \hat{j} + 3 \hat{k}) = 8 + (- 3) = 5 J$

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