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14. The weight density (lb.s/ft3) of a sphere with radius 10ft is inversely proportional to the distance from the bo...
Electric charge is distributed over the xy-plane, with density inversely proportional to the distance from the...
Electric charge is distributed over the xy-plane, with density inversely proportional to the distance from the origin. Show that the total charge inside a circle of radius R centered at the origin is proportional to R. What is the constant of proportionality?
2. Find the center of mass of the solid inside the sphere of radius a >...
2. Find the center of mass of the solid inside the sphere of radius a > 0, above z= 0, and below x2 + y2 given that the density is inversely proportional 3 to the distance squared from the origin.
10. The temperature T in a metal ball is inversely proportional to the distance from the center o...
10. The temperature T in a metal ball is inversely proportional to the distance from the center of the ball. which we take to be the origin. Show that at any point (r, y, z) in the ball, the direction of greatest increase in temperature is given by a vector that points toward the origin. 11 ot fhe a differentiable function.
10. The temperature T in a metal ball is inversely proportional to the distance from the center of the...
Question A1 (12 marks] A sphere with radius R carries a charge density that is proportional...
Question A1 (12 marks] A sphere with radius R carries a charge density that is proportional to the square of the distance from the origin, i.e. p = kr2 for some constant k. (a) [3 marks] Calculate k if the total charge on the sphere is Q. (Hint: dt = r2 sin(O) dr do do ) (b) [3 marks) Write down Gauss's law in integral form. In which situations can it be used to directly calculate the electric field of...
3. A ball, a solid sphere of radius r and mass m, is positioned at the top of a ramp that makes an angle of 0 with the horizontal. The initial position of the sphere is at a distance of d from its fi...
3. A ball, a solid sphere of radius r and mass m, is positioned at the top of a ramp that makes an angle of 0 with the horizontal. The initial position of the sphere is at a distance of d from its final position at the bottom of the incline. a) Find the velocity of the ball at the bottom of the ramp in terms of m, r, d, 8, and g. The moment of inertia of a sphere...
A solid sphere of uniform density starts from rest and rolls without slipping a distance of...
A solid sphere of uniform density starts from rest and rolls without slipping a distance of d = 2 m down a θ = 20° incline. The sphere has a mass M = 5.8 kg and a radius R = 0.28 m. 1. Of the total kinetic energy of the sphere, what fraction is translational? KE tran/KEtotal 2)What is the translational kinetic energy of the sphere when it reaches the bottom of the incline? KE tran = 3. What is the...
6. (extra credit) Find the center of mass of a region inside a circle of radius a if the density at any point is proportional to its distance from the center. (Either compute the center, or guess it...
6. (extra credit) Find the center of mass of a region inside a circle of radius a if the density at any point is proportional to its distance from the center. (Either compute the center, or guess it and give a theoretical argument why your guess is correct.)
6. (extra credit) Find the center of mass of a region inside a circle of radius a if the density at any point is proportional to its distance from the center. (Either...
Q3: Find the electric field inside a spherical sphere which carries a charge density proportional to...
Q3: Find the electric field inside a spherical sphere which carries a charge density proportional to the distance from the origin ? = fr, for someme constant f. (As you can see this charge density is not uniform, and you must integrate to get the enclosed charge)
A sphere of radius a is made of a nonconducting material that has a uniform volume charge density p.
A sphere of radius a is made of a nonconducting material that has a uniform volume charge density p. A spherical cavity of radius b is removed from sphere which is a distance z from the center of the sphere. Assume that a > z + b. a) Find the magnitude and direction of the electric field at point y0 which is separated by distance yo from the center of the sphere. b) Find the magnitude and direction of the electric field...
(14 points) (A) Consider a solid cone of height H and radius R having non-uniform composition...
(14 points) (A) Consider a solid cone of height H and radius R having non-uniform composition with volume mass density proportional to the distance from the central axis, reaching a maximum of do on the surface. Compute the total mass. (B) Consider a solid sphere of radius R having non-uniform composition with volume mass density proportional to the the distance from the surface, reaching a maximum do at the center. Compute the total mass.
2. Find the center of mass of the solid inside the sphere of radius a > 0, above z= 0, and below x2 + y2 given that the density is inversely proportional 3 to the distance squared from the origin.
10. The temperature T in a metal ball is inversely proportional to the distance from the center of the ball. which we take to be the origin. Show that at any point (r, y, z) in the ball, the direction of greatest increase in temperature is given by a vector that points toward the origin. 11 ot fhe a differentiable function.
10. The temperature T in a metal ball is inversely proportional to the distance from the center of the...
Question A1 (12 marks] A sphere with radius R carries a charge density that is proportional to the square of the distance from the origin, i.e. p = kr2 for some constant k. (a) [3 marks] Calculate k if the total charge on the sphere is Q. (Hint: dt = r2 sin(O) dr do do ) (b) [3 marks) Write down Gauss's law in integral form. In which situations can it be used to directly calculate the electric field of...
3. A ball, a solid sphere of radius r and mass m, is positioned at the top of a ramp that makes an angle of 0 with the horizontal. The initial position of the sphere is at a distance of d from its final position at the bottom of the incline. a) Find the velocity of the ball at the bottom of the ramp in terms of m, r, d, 8, and g. The moment of inertia of a sphere...
6. (extra credit) Find the center of mass of a region inside a circle of radius a if the density at any point is proportional to its distance from the center. (Either compute the center, or guess it and give a theoretical argument why your guess is correct.)
6. (extra credit) Find the center of mass of a region inside a circle of radius a if the density at any point is proportional to its distance from the center. (Either...
Q3: Find the electric field inside a spherical sphere which carries a charge density proportional to the distance from the origin ? = fr, for someme constant f. (As you can see this charge density is not uniform, and you must integrate to get the enclosed charge)
(14 points) (A) Consider a solid cone of height H and radius R having non-uniform composition with volume mass density proportional to the distance from the central axis, reaching a maximum of do on the surface. Compute the total mass. (B) Consider a solid sphere of radius R having non-uniform composition with volume mass density proportional to the the distance from the surface, reaching a maximum do at the center. Compute the total mass.
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