Concept explainers
Hydraulics
In Exercises 43–-46, determine the location of the horizontal axis
where
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
Calculus: Early Transcendental Functions (MindTap Course List)
- Center of mass of a curved wire A wire of densityd(x, y, z) = 15√y + 2 lies along the curve r(t) = (t2 - 1)j +2t k, -1 … t … 1. Find its center of mass. Then sketch the curveand center of mass together.arrow_forwardUsing Green's Theorem, find the outward flux of F across the closed curve C.F = xy i + x j; C is the triangle with vertices at (0, 0), (4, 0), and (0, 2)arrow_forwardUsing the Divergence Theorem, find the outward flux of F across the boundary of the region D.F = (y-x) i + (z-y) j + (z-x) k ; D: the region cut from the solid cylinder x 2 + y 2 ≤ 49 by the planes z = 0 and z=2 a) 0 b) 98π c) -98π d) -98arrow_forward
- Use Stokes' Theorem to find the work done on a particle moves along the line segments from the origin to the points (2,0,0) (2,4,3) , (0,4,3). and back to the origin. Note that this (counterclockwise) path is a rectangle on the plane z = 3/4 y. The motion is under the influence of the force field F = z2 i+ 2xy j + 4y2 karrow_forwardFlux of a vector field? Let S be a closed surface consisting of a paraboloid (z = x²+y²), with (0≤z≤1), and capped by the disc (x²+y² ≤1) on the plane (z=1). Determine the flow of the vector field F (x,y,z) = zj − yk, in the direction that points out across the surface S.arrow_forwardFlux across hemispheres and paraboloids Let S be the hemispherex2 + y2 + z2 = a2, for z ≥ 0, and let T be the paraboloid z = a - (x2 + y2)/a, for z ≥ 0, where a > 0. Assume the surfaces have outward normal vectors.a. Verify that S and T have the same base (x2 + y2 ≤ a2) and thesame high point (0, 0, a).b. Which surface has the greater area?c. Show that the flux of the radial field F = ⟨x, y, z⟩ across S is 2πa3.d. Show that the flux of the radial field F = ⟨x, y, z⟩ across T is 3πa3/2.arrow_forward
- The figure shows the side view of a portable traffic signal. The upper portion of the signal with attached frame has a mass of 90 kg with mass center at G. The signal and frame are hinged at point E and rest on a vertical post at H. In operation, member DEH is positioned vertically by means of the hand-operated winch so that the lights are directed to the left. Determine the necessary input force F that will just start to rotate the signal from its horizontal position. Note that handle A is rigidly attached to gear B. The dimension (AB) ̅=200 mm.arrow_forwardConsider the motion of a soccer ball that is kicked from the point x0,y0=⟨0,0⟩ with an initial velocity of u0,v0=⟨35,9⟩ m/s. Assume the x-axis is horizontal, the positive y-axis is vertical (opposite g), the ground is horizontal, and only the gravitational force acts on the object. Determine the maximum height of the soccer ball.arrow_forwardGauss’s law says that the electric flux through any closed surface is equal to the total chargecontained in the closed surface divided by the permittivity of free space, E0Find the charge contained inside a cube with vertices at (±1, ±1, ±1) when E =< x, y,z >arrow_forward
- 3. Find the coordinates of the centroid of the triangle enclosed by x = 1, y = 0,and y = 4x.arrow_forwardy = ex, y = 0, x = 0, x = 3 Find the exact coordinates of the centroid. (x, y) =arrow_forwardAn Eulerian flow field is described in Cartesian coordinates by V = 4i+xzj+5y3tk. (a) Is it compressible? (b) Is it steady? (c) Is the flow one-, two- or three-dimensional? (d) Find the y-component of the acceleration. (e) Find the y-component of the pressure gradient if the fluid is inviscid and gravity can be neglected.arrow_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