Finding Work in a Conservative Force Field In Exercises 19-22, (a) show that
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
Multivariable Calculus
- +y -n CI Č2 FIGURE Q3(b)arrow_forwardUse Green's theorem to calculate the work done by the force F(x, y) = xy'i + 3x?yj on a particle that is moving counterclockwise around the triangle with vertices (-3, 0), (0, 0), and (0, 3).arrow_forwardUse Green's Theorem to find the work done by the force F(x, y)= x(x + y)i + xy2j in moving a particle from the origin along the x-axis to (2, 0), then along the line segment to (0, 2), and then back to the origin along the y-axis.arrow_forward
- Unit Radial Vector Fields Show that f(x, y, z) = r = /x²+ y2 + z² х у г is a potential function for the unit radial vector field e, = That is, e, = Vr.arrow_forward(b) Find the work done by force field F = 3x? î + y²j on a particle when it moves from (0, 0) to (-T, 0) along the curves Cl and C2 in Figure Q3 (b) by solving S. F dr. Based on your calculation, judge whether the force, F is conservative or non- conservative and give your explanation. | -TT C1 0, C2 FIGURE Q3(b)arrow_forwardUse Green's theorem to find the work done by the force field F(xy) - хyі + x²+> on a particle that moves along the path that starts from the point (5,0), transverse the upper semi-circle x² + y? = 25 and return to the staring point along the x-axis. %3Darrow_forward
- 10) Find the work done by the force field F(x,y,z) = zi + x j + y k in moving a particle from the point (3, 0, 0) to the point (0,TT/2,3) along (a) straight line (b) the helix x = 3 cost, y = t, z = 3 sintarrow_forwardHow do you graph the vector field F = ⟨ƒ(x, y), g(x, y)⟩?arrow_forwardSketch the vector field represented by F (x, y) = (-x,y)arrow_forward
- Proj,u =|u/coso- 1=\u[coso u: V V Scal, u = |u|cose = u: V y. V (a) Find the length of the projection of w onto v given that w = (4, 7) and v = (1, 1). (b) A given force F = i+j- k (in newtons) moves an object from point (4, 7,2) to point (8, 3, 6) (in meters). Determine the work done by the force in moving the object.arrow_forwardElectric potential The potential function for the force field due to 1_ 4 4T€, |r|' the position vector of a point in the field, and ɛ, is the permittivity a charge y at the origin is o where r = (x, y, z) is of free space. a. Compute the force field F = -Vp. b. Show that the field is irrotational; that is, show that V xF = 0.arrow_forwardFind the work done by the force field F in moving an object from P to Q. F(x, y) = (2x + y)i + xj; P(1, 1), Q(6, 5) Need Help? Read Itarrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning