Find the center of gravity of a very thin right circular conical shell of base-radius r...
4. Find the center of mass of a homogeneous solid right circular cone if the density varies as the square of the distance. (from apex) 5. Find the center of gravity of a very thin right circular conical shell of base-radius r and altitude h.
A very thin circular hoop of mass(m) and radius(r) rolls without slipping down a ramp inclined at an angle(theta) with the horizontal, as shown in the figure.What is the acceleration(a) of the center of the hoop? Express your answer in terms of some or all of the variablesm,r, theta, and the magnitude of the acceleration due to gravity(g).
(a) Consider a uniformly charged, thin-walled, right circular cylindrical shell having total charge Q, radius R, and length l. Determine the electric field at a point a distance d from the right side of the cylinder as shown in Figure P23.46. Suggestion: Use the result of Example 23.8 and treat the cylinder as a collection of ring charges, (b) What If? Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume....
4. Use the AM-GM inequality to find the largest right circular cylinder that is inscribed in a right cone with base radius R and height H. Also determine the radius and height of the largest such cylinder. 4. Use the AM-GM inequality to find the largest right circular cylinder that is inscribed in a right cone with base radius R and height H. Also determine the radius and height of the largest such cylinder.
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...
Problem 5. a. Consider a uniformly charged thin-walled right circular cylindrical shell having a total charge Q radius R, and height h. Determine the electric field at a point a distance d from the right side of he cylinder as shown in the figure. a solid cylinder with the same dimensions and carrying the same charge, uniformly ed throughout its volume. Find the electric field it creates at the same point dx
Consider a uniformly charged, thin-walled, right circular cylindrical shell having total charge Q, radius R, and length l. Determine the electric field at a point a distance d from the right side of the cylinder as shown in the figure. Show that you recover the same expression if the cylinder is treated as a collection of ring charges. Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume. Find the field...
Problem 3. A table consists of a horizontal thin uniform circular disk of radius R and mass M, supported on its rim by three thin vertical legs that equidistant from each other. The are acceleration due to gravity is g. suddenly removed. Find the force exerted by the third leg on (a) Suppose two of the legs are the table top immediately after. [20 points] (b) Suppose instead that just one of the legs is suddenly removed. Find the force...
8. A right circular cylinder is inscribed in a sphere of radius v3. Find the dimensions of the cylinder if its volume is to be maximized. Hints: Let r be the distance from the center of the sphere to the base of the cylinder and let r be the radius of the base of the cylinder. Note that the height of the cylinder is 2r. 8. A right circular cylinder is inscribed in a sphere of radius v3. Find the...
Problem 6a: A non-conducting thin shell in the shape of a hemisphere of radius R centered at the origin has a total charge Q spread uniformly over its surface. The hemisphere is oriented such that its base is in the (y.z) plane. al. Find an expression for the surface charge density η. a2. Find the electric field at the center of the hemisphere, i.e. at x-0. Hint: consider the hemisphere as a stack of rings