Cylinder drop a uniform cylinder of mass m = 2kg railings r = 0.1m (and l=1/2 mr

Question

Cylinder drop a uniform cylinder of mass m = 2kg railings r = 0.1m (and l=1/2 mr^2) has a mass less frictionless siring wrapped around the outside and subsequently dropped from rest. The cylinder will fall and the siring will unwind like a yo-yo. The string will have some tension T during this process Find the net force rating in the cylinder (in terms of T if necessary ) Using sigma F = sigma r = 10, and premiering that find the lesion in the string What is the downward acceleration of the cylinder? Note that result does net depend on r or m

Explanation / Answer

a) the T is acting upwards and the mass mg acts downwards.

so, net force = T - mg

b) the mg force acts at the centre so it wont create any torque,

the torque will be provided by T

so , net torque will be

tau = T*R

c) now,

T - mg= ma ................(1)

and T*r = I * alpha

=>T*r = I * (a/r)

=> T*r= 0.5*m * r2 (a/r )

=> T = 0.5 ma

so , from (1) we have ,

0.5ma - mg= ma

=>0.5 a= -g

=> a = -2g

= -19.6 m/s2

c) now tenstion T = 0.5 ma = 9.8 N

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