The pulley in the figure has a radius R, moment of inertia I and an effectively
ID: 2202925 • Letter: T
Question
The pulley in the figure has a radius R, moment of inertia I and an effectively frictionless axle. A light string connects both masses via the pulley and doesn?t slip relative to the pulley. The coefficient of kinetic friction between block A and the tabletop is ?k. The system is released from rest, and block B descends. Block A has mass mA and block B has mass mB. (b) Find an expression for the speed of block A in terms of some or all of the variables mentioned above and d, the distance it has traveled.
Explanation / Answer
let T1 be the tension between the pulley and the block B T2 be tension between pulley and the block A mb*g-T1=mb*a T2-muk*ma*g=ma*a (T2-T1)*R=I*a/R T2-T1=I*a/R^2 (mb-muk*ma)*g=a[ma+mb-I/R^2] a=[mb-muk*ma]*g/[ma+mb-I/R^2] v^2=2ad v=sqrt(2ad)=sqrt[2dg*(mb-muk*ma)/(ma+mb-I/R^2)]
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