Ncert Exercises & Solutions

A body constrained to move along the z-axis of a coordinate system is subject to a constant force $\vec{F}$ given by $\vec{F} = - \hat{i} + 2 \hat{j} + 3 \hat{k} N$

Where $\hat{i}, \hat{j}, \hat{k}$ are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis?

Force exerted on the body, $\vec{F} = - \hat{i} + 2 \hat{j} + 3 \hat{k} N$

Displacement, $\vec{s}$ = $4 \hat{k}$ m

Work done, $W = \vec{F} . \vec{s}$
$= (- \hat{i} + 2 \hat{j} + 3 \hat{k}) . (4 \hat{k})$
$= 0 + 0 + 3 x 4 = 12 J$

Hence, 12 J of work is done by the force on the body.

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