First slide

Work done by Diff type of forces

Question

A force of $\vec{F} = 2 x \hat{i} + 2 \hat{j} + 3 z^{2} \hat{k}$ N is acting on a particle. Find the work done by this force in displacing the body from (1, 2,3) m to (3, 6, 1) m.

Moderate

A

-10 J
B

100 J
C

0.01 J
D

1 J

Solution

$W = \int_{x_{1}}^{x_{2}} F_{x} dx + \int_{y_{1}}^{y_{2}} F_{y} dy + \int_{z_{1}}^{z_{2}} F_{z} dz$
= $\int_{1}^{3} 2 xdx + \int_{2}^{6} 2 dy + \int_{3}^{1} 3 z^{2} dz$
= $(3^{2} - 1^{2}) + 2 (6 - 2) + (1^{3} - 3^{3})$
= - 10 J

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