Must show all work and calculations!!!! A primitive yo-yo is made by wrapping a

Question

Must show all work and calculations!!!! A primitive yo-yo is made by wrapping a string several times around a solid cylinder with m=200g and r=10cm. You hold the end of the string stationary while releasing the cylinder with no initial velocity. The string unwinds but doesn't slip or stretch as the cylinder drops and rotatess. In all calcs take g=10m/s^2 The moment of intertia for the cylinder is MR^2/2. A.) Find the tension in the string and the acceleration of the cylinder? B.) Find the speed of the center of mass of the cylinder after it has dropped a distance h =1.2m. Must show all work!!!!

Explanation / Answer

let the accn be a and ang. accn. be d ...so we have a= Rd as no slipping ...

=> eqns of motion => mg-T = ma and TR =.5(MR^2)d => T = .5Ma

so we get a = 2g/3 = 6.67 m/s^2 and T = .67 N

B) let the speed be v ... so ang. speed = v/R ....

so total energy gained = .5mv^2+ .5(.5mR^2)w = .75mv^2 = mgh (energy conservation)

=> v = 3.96 m/s

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