Question
An object moving in a liquid experiences a linear drag force: /vecD ( bv direction opposite the motion), where is a constant called the drag coefficient. For a sphere of radius R the drag constant can be computed as b = 6/pi/etaR , where /eta is theviscosityof the liquid a)Find an algebraic expression for v/rmx/kern1pt/left(t/right) , 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 v0 through a liquid of viscosity /eta . Express your answer in terms of the variables v0 , /eta , R , t , m , and appropriate constants. b)Water at 20 /circ/rmC has viscosity /eta = 1.0/times10^-3/emN/,/rms/m^2 . Suppose a 4.9- /rmcm -diameter, 31 /rmg ball is shot horizontally into a tank of 20 /circ/rmC water. How long will it take for the horizontal speed to decrease to 50 of its initial value? Express your answer using two significant figures.
Explanation / Answer
a) m g = 6 pi n R v v = m g / 6 pi n R b) v = m g / 6 pi n R v = p V g / 6 pi n R v = p 4 pi d^3 / 3 4 6 pi n R v = p d^3 / 18 n R v = p d^3 / 9 n d b = p d^2 / 9 n d = v t t = d / v t = 9 d n / p d^2 then plug and chug