8) A mass m=1 kg ishanging on a string wrapped around a thin cylindrical shell o

Question

8) A mass m=1 kg ishanging on a string wrapped around a thin cylindrical shell of radius R=0.2 meters. Neglect the mass of the string.

A) the mass falls with a constant linear accelertaion of a=2 m/s^2. there is no slippage between the string and the wheel. find the angular acceleration a of the whell.

B) upon releasing the mass m from rest, what is the angular velocity w of the wheel after 5 complete revolutions?

C) through the application of newtons 2nd law , determine the tension T in the string.

Explanation / Answer

 acceleration / radius = angular acceleration

angular acceleration a= 2/0.2 = 10 rad/s2

= 5 x 2 = 10

= (2a)

= ( 2 x 1 x 10) = 7.92 rad/s

M x g - T = M x acceleration

T = M x (g - acceleration)= 1(9.8 - 2)

T = 7.8 N      *****answer****

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