umatisi6ar

2023-03-11

How to find done in moving a particle P (0,0) to Q(4,7) if the magnitude and direction of the force is given by $v=<1,4>$?

stunaire2dt

Suppose that, under the influence of a force $\stackrel{\to }{F},$ a particle
moves from point $P$ to point $Q$
Then, the work $W$ done is given by, $W=\stackrel{\to }{F}\cdot \stackrel{\to }{PQ}$
We have, $\stackrel{\to }{F}=\left(1,4\right)$ and for the displacement $\stackrel{\to }{PQ}$
$\stackrel{\to }{PQ}=Q\left(4,7\right)-P\left(0,0\right)=\left(4,7\right)$
$\therefore W=\left(1,4\right)\cdot \left(4,7\right)=\left(1\right)\left(4\right)+\left(4\right)\left(7\right)=4+28=32\phantom{\rule{1ex}{0ex}}\text{unit}$

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