An object moving in a liquid experiences a linear drag, Ask an Expert

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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?

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