First slide

Work

Question

A force $\vec{F} = (4 \vec{i} - 3 \vec{j} + 7 \vec{k}) N$ moves a particle from $(\hat{i} + \hat{j} + \hat{k}) m$ to $(2 \hat{i} + 3 \hat{j} - 5 \hat{k}) m$ . The work done by the force is

Moderate

A

44J
B

-44J
C

8J
D

-36J

Solution

$\begin{array}{l} W = \vec{F} \cdot \vec{Δr} = [4 \hat{i} - 3 \hat{j} + 7 \hat{k}] \cdot [(2 \hat{i} + 3 \hat{j} - 5 \hat{k}) - (\hat{i} + \hat{j} + \hat{k})] \\ W = (4 \hat{i} - 3 \hat{j} + 7 \hat{k}) \cdot (\hat{i} + 2 \hat{j} - 6 \hat{k}) \\ W = 4 - 6 - 42 = - 44 J \end{array}$

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