10. -15 points SerPSE10 7.7.P.033.MI. A force acting on a particle moving in the
ID: 1880833 • Letter: 1
Question
10. -15 points SerPSE10 7.7.P.033.MI. A force acting on a particle moving in the xy plane is given by F (2 + x"j), where F is in newtons and x and y are in meters. The particle moves from the origin to a final positi having coordinates x4.50 m and y-4.50 m, as shown in the figure below (x, y x(m) (a) Calculate the work done by F on the particle as it moves along the purple path (000) (b) Calculate the work done by F on the particle as it moves along the red path (oBO) e Calkulate the work done by F on the particle as it moves along the blue path (oG (d) Is F conservative or nonconservative? O nonconservative O conservative (e) Explain your answer to part (d)Explanation / Answer
10. given force acting on particlekmoving in xy plane is
F = 2yi + x^2j
final position = (4.5, 4.5) m
a. path OAC
work done by F = W
dW = F.(dxi + dyj)
dW = 2ydx + x^2dy
integrating
W = 0 + 4.5^2*4.5 = 91.125 J
b. path OBC
dW = 2ydx + x^2*dy
integrating
W = 0 + 2*4.5*4.5 = 40.5 J
c. path OC
dW = 2ydx + x^2*dy
now for this path
y = x
hence
dx = dy
hence
dW = (2x + x^2)dx
integrating
W = (4.5^2 + (4.5^3)/3) = 50.625 J
d. hence we can see, W depends on path and hence F is non conservative
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