Question 2 A thin plate in the shape of the region in gray in the figure...
QUESTION 2 [25 marks] Figure 2 depicts a thin plate where its shape is the region, R bounded by the graphs y 3 and yx2. If the density distribution function of a thin plate is given by p(x, y) -1 2y 6x2, show the fastest way to find the centre of mass. Note: show your detailed calculation steps. a) (12 marks) -4 -2 Figure 2 b)x, y)represents a velocity field of a fluid over a surface S defined by z...
Find the center of mass of the lamina (thin plate) corresponding to the region 0 lessthanorequalto y lessthanorequalto 4 - x^2 in the xy plane if the density of the plate is proportional to the distance from the r axis.
Question A thin plate has been bent so as to take the shape of the area pasameleared by R (av) = (2-4 Joos fu? tujt (2-us en (v) & with - 1 4 UK 1 and OSVK 2T Si The density of the plate is proportional to Ho C distance to its left end ; that is, the plane ly= Determine the center of mass of the plate & the m= Sss 3 the da = dudu Follow the steps...
Center of Mass: Thin plate (region in the plane). Suppose R is the region bounded by the graph of f(x) = 6x- 2x2 and below by the graph of g(x) = x over the interval [2, 4]. Find the center of mass of the region. Assume that the region has a constant density δ.
A thin plate has been bent so as to take the shape of the surface parameterized by R(u, v) = (2 – u/2) cos(u)i + uj + (2 – u²/2) sin(v)k with -1 su s 1 and 0 svs 2n. This surface is shown below. 20- The density of the plate is proportional to the distance to its left end, i.e. the plane y = -1. Determine the center of mass of the plate. First give your answer exactly, then...
Find the center of mass of a thin plate covering the region between the curve y = 5 x2 and the x-axis from x = 1 to x = 4. The density of the plate is 8(x) = x(7). Graph the region. Show the rectangle and it's center of mass point (ã, Ý). Plot the center of mass of the plate (,y).
X2 Find the center of mass of a thin plate covering the region between the curve y = 43 and the x-axis from x = 1 to x = 4. The density of the plate is 8(x) = x(3). Graph the region. Show the rectangle and it's center of mass point (m,ỹ). Plot the center of mass of the plate (,y).
(2) Consider a thin plate with constant density 8 covering the region below the curve y = above the z-axis, and left of the line r = 9. r, Set up integrals that will give the mass of the plate, the moment about the z-axis, and the moment about the y-axis. Calculate the center of mass of the plate.
Question 6: Moment of inertia of an algebraic shape A plate of uniform areal density p= 4 kg/m2 is bounded by the four curves: y= -x2 – 2x – 4 m y=-23c2 + 4x + 19 m x = -2 m x = -1 m, where x and y are in meters. Point P has coordinates Pc = -1 m and Py = –3 m. What is the moment of inertia Ip of the plate about point P? Ip =...
4. Two students were asked to find the center of mass of a thin plate of constant density 8 covering the region bounded above by y = x - 22 and below by y = -2. The center of mass of a typical vertical strip is represented by (6,5) (see figure). Both students agree that the mass differential dm = 8 dA = density. length width should be dm = 8. (-)-(-x).da. (a) Student 1 claims that (č, ) is...