Mass In Exercises 23 and 24, find the total mass of a spring with density
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Calculus: Early Transcendental Functions
- Calculate the fluid force on one side of the plate using the coordinate system shown below. Assume the density is 62.4 lb/ft³. y (ft) Surface of pool HA ►x (ft) Depth -y=-1 |y| (x,y) - 11 The fluid force on one side of the plate is lb.arrow_forwardMoment of inertia about y-axis of a square plate with surface density f(x, y)= k = constant and vertices with coordinates (0,0), (0.2), (2.0) and (2.2) points ? 14 k 3 A) 16 k 3 В) 13 -k 3 10 D) 3 11 E) 3arrow_forwardPlease provide Handwritten answer. Advanced Math We consider a thin plate occupying the region D located in the upper half-plane (where y ≥ 0) and between the parabolas of equations : y = 2 - x2 and y = 1 - 2x2 The density of the plate is proportional to the distance from the x axis. a) Calculate the moments of inertia (second moments) of the plate with respect to the coordinate axes.b) Is it easier to rotate the plate around the x-axis or the y-axis? Justify your answer.arrow_forward
- Calculate the fluid force on one side of the plate using the coordinate system shown below. Assume the density is 62.4 The fluid force on one side of the plate is lb/ft³. lb. (...) y (ft) Surface of pool ►x (ft) Depth -y = -2 |y| (x,y) - 12 Carrow_forwardA fluid has density 900 kg/m³ and flows with velocity v = xi+yj + zk, where x, y, and z are measured in meters, and the components of 7 are measured in meters per second. Find the rate of flow outward through the part of the paraboloid z = 64 x² - y² that lies above the xy plane. - Submit Question kg/s Question Help: Video Message instructorarrow_forwardThe vertical stern of a boat partially submerged in seawater with a superimposed coordinate system is shown in the figure. The table shows the widths w of the stern (in feet) at indicated values of y. Use the Midpoint Rule with n = 4 to approximate the fluid force against the stern.arrow_forward
- Use spherical coordinates. Let H be a solid hemisphere of radius 5 whose density at any point is proportional to its distance from the center of the base. (Let K be the constant of proportionality.) (a) Find the mass of H. (b) Find the center of mass of H. (Assume the upper hemisphere of a sphere centered at the origin.) (x, y, z) = ( (c) Find the moment of inertia of H about its axis Iz =arrow_forwardA fluid has density 1100 kg/m³ and flows with velocity v = xi + yj + zk, where x, y, and z are measured in meters, and the components of are measured in meters per second. Find the rate of flow outward through the part of the paraboloid z = 49 - x² - y² that lies above the xy plane. kg/s Question Help: Video Submit Question Jump to Answerarrow_forward2 A circular wire hoop of constant density 8=3 lies along the circle x² + y² = 7a² in the xy-plane. Find the hoop's moment of inertia, I2, about the z-axis. The hoop's moment of inertia about the z-axis is l₂ = (Type an exact answer, using it as needed.)arrow_forward
- Calculate the fluid force on one side of the plate using the coordinate system shown below. Assume the density is 62.4 Ib/ t3 The fluid force on one side of the plate is Ib. y (f) ...... x (f) Surface of pool Depth lyl - 3 xy)arrow_forwardA lamina with constant density p(x, y) = 2p occupies the given region. Find the moments of inertia I, and I, and the radii of gyration x and y. the triangle with vertices (0, 0), (b, 0), and (0, 3h) = x =arrow_forwardA joint between two concrete slabs A and B is filled with a flexible epoxy that bonds securely to the concrete (see figure). B A B The height of the joint is h = 4.5 in., its length is L = 47 in., and its thickness is t = 0.9 in. Under the action of shear forces V, the slabs displace vertically through the distance d = 0.005 in. relative to each other. (a) What is the average shear strain yver in the epoxy? (Enter the magnitude in rad.) rad (b) What is the magnitude of the forces V (in kips) if the shear modulus of elasticity G for the epoxy is 140 ksi? kipsarrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,