1)A primitive yoyo is constructed of a string wound around the edge of a solid c

Question

1)A primitive yoyo is constructed of a string wound around the edge of a solid cylinder (M) and a small mass (m) attached to the free end of the string. The cylinder is free to rotate about the central axis with out friction. if Rcyclinder=12cm, M=400g and m=50g, find the speed of the small mass after it has descended 50cm starting from rest. (Hint Use conversation of energy principles)

2) An atwood machine is constructed of a large pulley of radius 0.05m, two hanging masses, .46kg and 0.5kg and a light cord connecting the masses over the pulley. When released from rest, the heavier block falls 0.75m in 5.00 seconds. a) What is the acceleration of the system? b) what is the magnitude of the pulleys angular acceleration?

c: Consider the pulley as a uniform disk and find its mass

Explanation / Answer

By applying conservation of energy

1) mgh =( mv^2+Iw^2)/2 where h=height descended by m, v = velocity of m , w is angular velocity of cylinder

v=Rw , I = MR^2 / 2

Subtituting in above eqn u get

mgh = (m+M/2)v^2 /2

V^2 = 4mgh/(M+2m) = 4(50*9.8*(0.5))/(400+2(50)) = 9.8/5 = 1.96 m/s

2) apply newton law of motion s= ut + at^2 / 2

u= 0 , t=5 , s= 0.75

a) So acceleration = 2s/t^2 = 2(0.75)/5^2 = 0.06 m/s2

b) angular acceleration = a/r = 0.06/0.05 = 1.2 s^-

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