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An object moving in a liquid experiences a linear drag force: D=(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=6pnR, where n is the viscosity of the liquid.
a. Use what you've learned in calculus to prove that ax=vxdvx/dx
b. Find an algebraic expression for vx(x), that the x-component of velocity as a function of distance traveled, for a spherical particle of radius R and mass m that is shot horizontally with initial speed v0 through a liquid of viscosity n.
c. Water at 20o C has a viscosity n=1.0x10-3 N s/m2. Suppose a 1.0-cm-diameter, 1.0 g marble is shot horizontally into a tank of 20o C water at 10 cm/s. How far will it travel before stopping?
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
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