Show that a force that does no work must be a velocity dependent force.
Show that a force that does no work must be a velocity dependent force.
As work done by force is zero,
$\therefore d \mathrm{~W}=\overrightarrow{\mathrm{F}} \cdot \overrightarrow{d l}=0$
$\therefore \overrightarrow{\mathrm{F}} \cdot \overrightarrow{d l} \cdot d t$
$\therefore \overrightarrow{\mathrm{F}} \cdot(\vec{v} \cdot \overrightarrow{d l})=0$
$\therefore \overrightarrow{\mathrm{F}} \cdot \vec{v}=0, d l \neq 0$
$\therefore$ F $v \cos \theta=0$
If $v$ changes direction then to make $\theta=90, \mathrm{~F}$ must charne angle according to $v .$ So, $\mathrm{F}$ is dependent on $v$ to make work done zero.
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