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 $\overrightarrow{PQ}$

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

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

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?

$A=\left[\begin{array}{ccccc}1& 5& -4& -3& 1\\ 0& 1& -2& 1& 0\\ 0& 0& 0& 0& 0\end{array}\right]$T must be a linear transformation, we assume. Can u find the T standard matrix.$T:{\mathbb{R}}^{2}\to {\mathbb{R}}^{4},T\left({e}_{1}\right)=(3,1,3,1)\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}T\left({e}_{2}\right)=(-5,2,0,0),\text{}where\text{}{e}_{1}=(1,0)\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}{e}_{2}=(0,1)$

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