1) a book of mass 3 kg rests on a plank. you tilt one end of the plank and slowl

Question

1) a book of mass 3 kg rests on a plank. you tilt one end of the plank and slowly increase the angle of the tilt. the coefficient of static friction between the book and the plank is .36. what is the maximun angle of tilt for which the book will remain stationary and not slide down the plank?

2) a spherical raindrop 3.5 mm in diameter falls through a vertical distance of 4300m. take the cross sectional area of the raindrop =pir^2, drag coefficient .45, density of water to be 1000kg/m^3, and density of air to be 1.2 kg/m^3.

a) calculate the speed a spherical raindrop would achieve falling from 4300m in the absence of air drag. m/s

b) what would its speed be at the end of 4300m when there is air drag? m/s

Explanation / Answer

1) at max angle

friction = u N

mg sin theta - friction = 0

u m g cos theta = m g sin theta

tan theta = u

theta = arctan(.36)=19.8 degrees

2) v^2 = v0^2 + 2 a x

v = sqrt(2*9.81*4300)=290.45 m/s

b) k A v - mg = 0

v terminal = 1000*(4/3*pi*(3.5E-3/2)^3)/(.45*pi*(3.5E-3/2)^2)=5.19 m/s

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