Respuesta :
Given data:
* The force acting on the particle is,
[tex]F=3.77\text{ i + 7.73 j}[/tex]* The displacement of the particle along the x-axis is,
[tex]\begin{gathered} dx=6.43-1.81 \\ dx=4.62\text{ m} \end{gathered}[/tex]* The displacement of the particle along the y-axis is,
[tex]\begin{gathered} dy=9.47-4.97 \\ dy=4.5\text{ m} \end{gathered}[/tex]Solution:
The displacement vector of the particle is,
[tex]\begin{gathered} d=\text{dx i + dy j} \\ d=4.62\text{ i + }4.5\text{ j} \end{gathered}[/tex]The work done on the particle in terms of the force and displacement vector is,
[tex]W=F\cdot d[/tex]Substituting the known values,
[tex]\begin{gathered} W=(3.77i+7.73j)\cdot(4.62i+4.5j) \\ W=17.42+34.78 \\ W=52.2\text{ J} \end{gathered}[/tex]Thus, the work done by the force on the particle is 52.2 J.
