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In the following integrals, remember that î î = j · j = 1 (a) The work is given by the following integral from the initial starting point i to the ending point f. î'j = 0. and W = We compute the integral for each displacement along the path. For the displacement from O to O, 4.15 (2yî + x?j) · (îdx) 4.15 Wo 4.15 4.15 2ydx 4.15 dx 4.15 2y where the y has been factored out of the integral because it is constant for this integration. Since along this path, y = 0, we have that o J. = 0

In the following integrals, remember that î î = j · j = 1 (a) The work is given by the following integral from the initial starting point i to the ending point f. î'j = 0. and W = We compute the integral for each displacement along the path. For the displacement from O to O, 4.15 (2yî + x?j) · (îdx) 4.15 Wo 4.15 4.15 2ydx 4.15 dx 4.15 2y where the y has been factored out of the integral because it is constant for this integration. Since along this path, y = 0, we have that o J. = 0

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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In the following integrals, remember that îj = 0. î î = j · j = 1 and (a) The work is given by the following integral from the initial starting point i to the ending point f. W = We compute the integral for each displacement along the path. For the displacement from O to O, 4.15 4.15 WOD (2yî + x?j) · (îdx) %3D 4.15 4.15 2ydx 4.15 4.15 = 2y dx: where the y has been factored out of the integral because it is constant for this integration. Since along this path, y = 0, we have that .ונ = 0 WOD
Transcribed Image Text:In the following integrals, remember that îj = 0. î î = j · j = 1 and (a) The work is given by the following integral from the initial starting point i to the ending point f. W = We compute the integral for each displacement along the path. For the displacement from O to O, 4.15 4.15 WOD (2yî + x?j) · (îdx) %3D 4.15 4.15 2ydx 4.15 4.15 = 2y dx: where the y has been factored out of the integral because it is constant for this integration. Since along this path, y = 0, we have that .ונ = 0 WOD
A force acting on a particle moving in the xy plane is given by F = (2yî + x2j), where F is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x = 4.15 m and y = 4.15 m, as shown in the figure below. у (m) (х, у) x (m) (a) Calculate the work done by F on the particle as it moves along the purple path (oO©). (b) Calculate the work done by F on the particle as it moves along the red path (OB©). (c) Calculate the work done by F on the particle as it moves along the blue path (o©). (d) IsI conservative or nonconservative? (e) Explain your answer to part (d).
Transcribed Image Text:A force acting on a particle moving in the xy plane is given by F = (2yî + x2j), where F is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x = 4.15 m and y = 4.15 m, as shown in the figure below. у (m) (х, у) x (m) (a) Calculate the work done by F on the particle as it moves along the purple path (oO©). (b) Calculate the work done by F on the particle as it moves along the red path (OB©). (c) Calculate the work done by F on the particle as it moves along the blue path (o©). (d) IsI conservative or nonconservative? (e) Explain your answer to part (d).
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