A metal sphere of radius r falls vertically at a speed v through a liquid. As...
A metal sphere of radius r falls vertically at a speed v through a liquid. As it falls, it experiences a drag force F which is given by F = Arv, where A is a constant. Determine the S.I. base units of the constant A.
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A metal sphere of radius r falls vertically at a speed v through
a liquid. As...
with A small particle of radius R and density p, moving at speed vin a viscous...
with A small particle of radius R and density p, moving at speed vin a viscous fluid of density dynamic viscosity n experiences a drag force given by Stokes' law F= 69Rv Find an expression for the terminal velocity of the particle as it falls through the fluid under the influence of gravity which includes Pp, pg, R, and n.
Problem 1: A grounded metal sphere with radius R is located at the center of a...
Problem 1: A grounded metal sphere with radius R is located at the center of a linear dielectric sphere with radius 2R. The dielectric has a relative permittivity of &r. The composite sphere is exposed to some external fields, which create a potential V-α cosa where α is a constant Find the electric field and the electric displacement in the dielectric, i.e. R<rc2R. Hint: Use the appropriate boundary (surface) conditions to solve for the potential in that region in terms...
When an object moves through a fluid, the fluid exerts a viscous force F on the...
When an object moves through a fluid, the fluid exerts a viscous force F on the object that tends to slow it down. For a small sphere of radius R, moving slowly with a speed v, the magnitude of the viscous force is given by Stokes, law, F = 6πηRv, where η is the viscosity of the fluid. (a) What is the viscous force on a sphere of radius R = 8.9 x 10-4 m falling through water (η =...
An object moving in a liquid experiences a linear drag force: D⃗ =(bv, direction opposite the...
An object moving in a liquid experiences a linear drag force: D⃗ =(bv, direction opposite the motion), where b is a constant called the drag coefficient. For a sphere of radius R, the drag constant can be computed as b=6πηR, where η is the viscosity of the liquid. Water at 20 ∘C has viscosity η=1.0×10−3Ns/m2. Suppose a 4.4-cm-diameter, 34 g ball is shot horizontally into a tank of 20 ∘C water. How long will it take for the horizontal speed...
A raindrop falls vertically through a stationary mist
A raindrop falls vertically through stationary mist, collecting mass as it falls. The raindrop remains spherical and the rate of mass accretion is proportional toits speed and the square of its radius. Show that, if the drop starts from rest with a negligible radius, then it has constant acceleration g/7. [Tricky ODE.]
A solid metal sphere of radius R carriers a charge-O where Surrounding this sphere is a...
A solid metal sphere of radius R carriers a charge-O where Surrounding this sphere is a metal shell of inner radius Ra and outer radius Rs that carriers a total charge ofQ- +8Q, as shown in right figure. Determine the electric field strengths at all values ofr.
(7%) Problem 14: A spherical rain drop of radius R and mass M falls vertically through...
(7%) Problem 14: A spherical rain drop of radius R and mass M falls vertically through a cloud layer. The drop enters the cloud layer at a height H from the ground and exits the cloud at a height h. While inside the cloud the drop accumulates water molecules so that its mass and size grow with time. The mass of the rain drop at time t when inside the cloud is given as follows: m(t) = M + at...
The terminal speed of a spherical particle falling in a liquid is given by 2R2g P-P)...
The terminal speed of a spherical particle falling in a liquid is given by 2R2g P-P) 91 v= where R is the radius of the sphere, p, is its density, p, is the density of the fluid, and n is the coefficient of viscosity. Using this equation, find the viscosity (in mPa s) of motor oil in which a steel ball of radius 0.7 mm falls with a terminal speed of 4.43 cm/s. The densities of the ball and the...
An object of mass m moves at a constant speed v in a circular path of radius r.
An object of mass m moves at a constant speed v in a circular path of radius r. The force required to produce the centripetal component of acceleration is called the centripetal force and is given by F=mv2/r. Newton's Law of Universal Gravitation is given by F=GMm/d2, where d is the distance between the centers of the two bodies of masses M and m, and G is a gravitational constant. The speed required for circular motion is v= √(GM/r). Use the...
A cylindrical cork of radius R and length L is floating in a liquid such that...
A cylindrical cork of radius R and length L is floating in a liquid such that its axis of symmetry is vertical and half of the length of the cork is below the fluid (the density of the fluid is p), as in Figure 2. For this problem, ignore any effects from friction, drag and the viscosity of the fluid (a) Show that the density of the cork, Pe is half that of the fluid (Pe ps) (b) If the...
with A small particle of radius R and density p, moving at speed vin a viscous fluid of density dynamic viscosity n experiences a drag force given by Stokes' law F= 69Rv Find an expression for the terminal velocity of the particle as it falls through the fluid under the influence of gravity which includes Pp, pg, R, and n.
Problem 1: A grounded metal sphere with radius R is located at the center of a linear dielectric sphere with radius 2R. The dielectric has a relative permittivity of &r. The composite sphere is exposed to some external fields, which create a potential V-α cosa where α is a constant Find the electric field and the electric displacement in the dielectric, i.e. R<rc2R. Hint: Use the appropriate boundary (surface) conditions to solve for the potential in that region in terms...
A solid metal sphere of radius R carriers a charge-O where Surrounding this sphere is a metal shell of inner radius Ra and outer radius Rs that carriers a total charge ofQ- +8Q, as shown in right figure. Determine the electric field strengths at all values ofr.
(7%) Problem 14: A spherical rain drop of radius R and mass M falls vertically through a cloud layer. The drop enters the cloud layer at a height H from the ground and exits the cloud at a height h. While inside the cloud the drop accumulates water molecules so that its mass and size grow with time. The mass of the rain drop at time t when inside the cloud is given as follows: m(t) = M + at...
The terminal speed of a spherical particle falling in a liquid is given by 2R2g P-P) 91 v= where R is the radius of the sphere, p, is its density, p, is the density of the fluid, and n is the coefficient of viscosity. Using this equation, find the viscosity (in mPa s) of motor oil in which a steel ball of radius 0.7 mm falls with a terminal speed of 4.43 cm/s. The densities of the ball and the...
A cylindrical cork of radius R and length L is floating in a liquid such that its axis of symmetry is vertical and half of the length of the cork is below the fluid (the density of the fluid is p), as in Figure 2. For this problem, ignore any effects from friction, drag and the viscosity of the fluid (a) Show that the density of the cork, Pe is half that of the fluid (Pe ps) (b) If the...
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