Homework Answers
Here we apply concept of calculus and integration to determine total mass of given shapes
![13 & for whole cone t varies from 0 tot AM = Jum = STR² I 23h | 0 6 a M = Sotka [44] M= 1 So #R² H ) I M = mass of cone. Sphe](http://img.homeworklib.com/questions/8b2df350-7175-11ea-aaa0-9f3ffc7b7dc7.png?x-oss-process=image/resize,w_560)
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(14 points) (A) Consider a solid cone of height H and radius R having non-uniform composition...
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 bas...
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...
A solid non-conducting sphere of radius R carries a uniform charge density throughout its volume. At...
A solid non-conducting sphere of radius R carries a uniform charge density throughout its volume. At a radial distance r1 = R/2 from the center, the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r2 = 3R?
In the figure the sphere of radius R is solid and non-conductive and has a uniform...
In the figure the sphere of radius R is solid and non-conductive and has a uniform charge volumetric distribution p0. A spherical shell with inner radius 2R and outer radius 3R is concentric with the sphere and unloaded. Find, in terms of p0 and R: a) the value of the electric charge in the sphere, b) the magnitude of the electric field at a radial distance r - 2.5R, c) the value of the surface charge density induced in the...
A charged sphere of radius R (see picture below) has non-uniform volume charge density that is...
A charged sphere of radius R (see picture below) has non-uniform volume charge density that is proportional to distance its center O: rho(r) = br where b is a positive constant of proper units. (Consider values of R and b to be known) What are the proper units for constant b? b) Find electric potential V_0 at the center O.
A solid right circular cone has radius 2 and height 4. Suppose the density of the...
A solid right circular cone has radius 2 and height 4. Suppose the density of the cone above has a density that varies as the square of the distance from the base. Find the center of mass.
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 rotate...
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...
A solid cylinder of height L and radius R has uniform mass density . Find the...
A solid cylinder of height L and radius R has uniform mass density . Find the moment of inertia tensor about the center of the cylinder. For what value of L/R is the cylinder equally easy to spin about any axis?
a non-conducting solid sphere of radius 8.5 centimeters has a uniform charge density. the magnitude of...
a non-conducting solid sphere of radius 8.5 centimeters has a uniform charge density. the magnitude of the electric field at 17 centimeters from the spheres center is 2.14×10^3 Newtons per Coulomb. a. what is the spheres volume charge density? b. find the magnitude of the electric field at a distance of 5 centimeters from the sphere center
9. Consider a non-conducting solid sphere of radius 2a and uniform charge density per unit volume...
9. Consider a non-conducting solid sphere of radius 2a and uniform charge density per unit volume Pv. 2a 2a (a) Detrmine the electric field everywhere (b) Plot the magnitude of the electric field (c) A spherical cavity of radius a is carved out from the sphere. Compute the electric field within the cavity
Problem 2 (6 points): Consider a solid sphere of radius R and uniform charge density p....
Problem 2 (6 points): Consider a solid sphere of radius R and uniform charge density p. Letr be the distance from the center of the sphere. It is helpful now to remind yourself what o(r) and E(F) are for this charge configuration. (a) Given the electric field E for the sphere, verify explicitly that XE = 0, both for r <R and r>R (3 points) (b) Show that V20= -p/c "CR T>R by expressing the electric potential o(r) in Cartesian...
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...
In the figure the sphere of radius R is solid and non-conductive and has a uniform charge volumetric distribution p0. A spherical shell with inner radius 2R and outer radius 3R is concentric with the sphere and unloaded. Find, in terms of p0 and R: a) the value of the electric charge in the sphere, b) the magnitude of the electric field at a radial distance r - 2.5R, c) the value of the surface charge density induced in the...
A charged sphere of radius R (see picture below) has non-uniform volume charge density that is proportional to distance its center O: rho(r) = br where b is a positive constant of proper units. (Consider values of R and b to be known) What are the proper units for constant b? b) Find electric potential V_0 at the center O.
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...
9. Consider a non-conducting solid sphere of radius 2a and uniform charge density per unit volume Pv. 2a 2a (a) Detrmine the electric field everywhere (b) Plot the magnitude of the electric field (c) A spherical cavity of radius a is carved out from the sphere. Compute the electric field within the cavity
Problem 2 (6 points): Consider a solid sphere of radius R and uniform charge density p. Letr be the distance from the center of the sphere. It is helpful now to remind yourself what o(r) and E(F) are for this charge configuration. (a) Given the electric field E for the sphere, verify explicitly that XE = 0, both for r <R and r>R (3 points) (b) Show that V20= -p/c "CR T>R by expressing the electric potential o(r) in Cartesian...
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