Chapter 6, Problem 76EAP

An object moving in a liquid experiences a linear drag force: $\stackrel{\to }{F}$_drag = (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 = 6p?R, where ? is the viscosity of the liquid.

a. Find an algebraic expression for v_x(t), the x-component of velocity as a function of time, for a spherical particle of radius R and mass m that is shot horizontally with initial speed v₀through a liquid of viscosity ?.

b. Water at 20°C has viscosity ? = 1.0 × 10-3 N s/m². Suppose a 4.0-cm-diameter, 33 g ball is shot horizontally into a tank of 20°C water. How long will it take for the horizontal speed to decrease to 50% of its initial value?