Question

find the work done on a particle moving from ( j ) to ( k ) if the magnitude and the direction of the force is given by ( mathbf{f} ).

( j=(0,-8), k=(-7,1), mathbf{f}=5 mathbf{i}+4 mathbf{j} )

Explanation:

Step1: Find the displacement vector \(\overrightarrow{JK}\)

The displacement vector \(\overrightarrow{JK}\) is given by \(\overrightarrow{JK}=(x_{K}-x_{J})\mathbf{i}+(y_{K}-y_{J})\mathbf{j}\).
Here, \(x_{J} = 0,y_{J}=-8,x_{K}=-7,y_{K}=1\).
So, \(\overrightarrow{JK}=(-7 - 0)\mathbf{i}+(1-(-8))\mathbf{j}=-7\mathbf{i}+9\mathbf{j}\)

Step2: Calculate the work done \(W\)

The work done \(W\) by a force \(\mathbf{F}=F_{x}\mathbf{i}+F_{y}\mathbf{j}\) over a displacement \(\mathbf{d}=d_{x}\mathbf{i}+d_{y}\mathbf{j}\) is given by \(W=\mathbf{F}\cdot\mathbf{d}=F_{x}d_{x}+F_{y}d_{y}\)
Given \(\mathbf{F} = 5\mathbf{i}+4\mathbf{j}\) and \(\mathbf{d}=\overrightarrow{JK}=-7\mathbf{i}+9\mathbf{j}\)
\(W=(5\times(-7))+(4\times9)\)
\(W=-35 + 36\)

Answer:

\(1\)