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

Beginner2023-03-12Added 7 answers

Suppose that, under the influence of a force $\overrightarrow{F},$ a particle

moves from point $P$ to point $Q$

Then, the work $W$ done is given by, $W=\overrightarrow{F}\cdot \overrightarrow{PQ}$

We have, $\overrightarrow{F}=(1,4)$ and for the displacement $\overrightarrow{PQ}$

$\overrightarrow{PQ}=Q(4,7)-P(0,0)=(4,7)$

$\therefore W=(1,4)\cdot (4,7)=\left(1\right)\left(4\right)+\left(4\right)\left(7\right)=4+28=32\phantom{\rule{1ex}{0ex}}\text{unit}$

moves from point $P$ to point $Q$

Then, the work $W$ done is given by, $W=\overrightarrow{F}\cdot \overrightarrow{PQ}$

We have, $\overrightarrow{F}=(1,4)$ and for the displacement $\overrightarrow{PQ}$

$\overrightarrow{PQ}=Q(4,7)-P(0,0)=(4,7)$

$\therefore W=(1,4)\cdot (4,7)=\left(1\right)\left(4\right)+\left(4\right)\left(7\right)=4+28=32\phantom{\rule{1ex}{0ex}}\text{unit}$