(1 point) Consider a right circular solid cone S standing on its tip at the origin. The height of...
Consider two right circular cones, cone A which is solid and cone B which is hollow and has mass only around the shell of the cone. Both cones have the same mass M , the same height H, and the same top radius R. Let the cone axes be along the y—axis with the tip at y=0 and the circular end at y=H. Which cone will have the largest moment of inertia?
1. Consider a solid cone with uniform density p, height h, and circular base with radius R (hence mass M,sphR2). Let the vertex of the cone be the origin ofthe body frame. By symmetry, choose basis vectors e for the body frame such that the inertia tensor I, is diagonal. Will this rigid body with this body origin be an asymmetric top, a symmetric top, or a spherical top? Calculate the inertia tensor in this basis How will the inertia...
Please help this one A right-circular cone with base radius r, height h, and volume ar," is positioned so that the base sits in the x-y plane with its center at the origin. The cone points upwards in the +z-direction. Starting from the definition, find and expression for the z-coordinate of the center of mass of a homogeneous right-circular cone. Verify the units and the magnitude of your answer to part (a) Briefly explain how you could experimentally verify your...
The region is a right circular cone, 2 = Var? + y2 with height 29. Find the limits of integration on the triple integral for the volume of the cone using Cartesian, cylindrical, and spherical coordinates and the function to be integrated. For your answers 0 theta, o=phi, and p = rho. Cartesian V = p(x, y, z) dz dy da where A C = B = ,F= E ,D= and p(x, y, z) = Cylindrical V = so" C"S"...
(1 point) The tank in the form of a right-circular cone of radius 9 feet and height 23 feet standing on its end, vertex down, is leaking through a circular hole of radius 3 inches. Assume the friction coefficient to be c = = 0.6 and g = 32ft/s2. Then the equation governing the height h of the leaking water is dh dt If the tank is initially full, it will take it seconds to empty.
4. a) A solid truncated cone with smaller radius a and larger radius b, height h, and Determine the moment of inertia of the truncated cone in terms of a,b.p and central axis. 8 pts h when rotated about its b) A bullet of with a mass-m,is fired into the cone with a speed v, in the z direction. The bullet a +b above the central axis of the cone and lodges in the cone at the enters the cone...
Previous Problem List Next (1 point) The tank in the form of a right-circular cone of radius 4 feet and height 29 feet standing on its end, vertex down, is leaking through a circular hole of radius 2 inches. Assume the friction coefficient to be c = 0.6 and g=32ft/. Then the equation governing the height h of the leaking water dh - seconds to If the tank is initially full, it will take it empty.
A rectangular solid of height h increases in optical density as its height increases, so the index of refraction of the solid increases with height according to: n(y) = 1.10(4.00y + 1.00) where y is the distance, in meters, from the origin (see diagram). A beam of light traveling in air (n = 1.00) in the x-y plane strikes the bottom of the tank at the origin, making an angle of incidence with the normal of ?1. Assume: n varies...
(1 point) The region W is the cone shown below. The angle at the vertex is #/3, and the top is flat and at a height of 3v3. Write the limits of integration for wdV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry): (a) Cartesian: With a = .b = .d = and f = e = Volume = / ddd (b) Cylindrical: With a = CE and f = ddd e...
1. Find the volume of the solid under the cone z= sqrt (x^2 + y^2) and over the ring 4 |\eq x^2 + y^2 |\eq 25. 2. Find the volume of the solid under the plane 6x + 4y + z= 12 and over the disk with border x^2 + y^2 = y. 3. The area of the smallest region, locked by the spiral r\Theta= 1, the circles r=1 and r=3 and the polar axis.