A force acting on a particle moving in the xy plane is given by F rightarrow = (

Question

A force acting on a particle moving in the xy plane is given by F rightarrow = (2y I + x2 J), where F rightarrow is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x = 4. 60 m and y 4. 60 m, as in the figure below. Calculate the work done by F rightarrow on the particle as it moves along the purple path (OAC). Calculate the work done by F rightarrow on the particle as it moves along the red path (OBC). Calculate the work done by F rightarrow on the particle as it moves along the blue path (OC). Is F rightarrow conservative or nonconservative? Explain your answer to part (d).

Explanation / Answer

a)& b) & c)W=F.S=(2y i+ x^2 j).(4.6 i+ 4.6 j)=9.2 y+4.6x^2 j=139.66 j [y=4.6,x=4.6] AS U CAN SEE FROM W=9.2 Y+4.6X^2 that work done depends upon scaler product which depends only upon final position of the particle . so a)&b)@c) are equal d)IT IS CONSERVATIVE FORCE BECAUSE WORK DONE IS PATH INDEPENDENT AND DEPENDS ONLY UPON FINAL POS

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