physics you make a primitive yo-yo by wrapping a string several times around the

Question

physics

you make a primitive yo-yo by wrapping a string several times around the edge of a solid disk of mass 0.300kg and radius 4.00cm. You hold the end of the string stationary while releasing the disk with no initial motion. The string unwinds wighout slipping or stretching as the disk drops and rotates. (a) use energy consideration to find the speed of the center of mass of the solid disk after it has fallen 0.5m (b) using rotional dynamics, find the tension in the cord. (c) what is the acceleration of the falling disk? show that tis is consistent the answer to (a)

Explanation / Answer

a) after it has fallen 0.5 m , it will got translational and rotational KE.

using energy conservation,

mgh = mv^2 /2 + Iw^2 /2

and I = m r^2 /2 for disc and w = v/r

mgh = mv^2 / 2 + (m r^2 /2 )(v/r)^2/2 = mv^2 / 2 + mv^2 / 4

mgh = 3 m v^2 / 4

9.81 x 0.5 = 3 x v^2 / 4

v = 2.56 m/s

b) using Fnet = ma on disc,

mg - T = ma   ... (i)

using torque = I x alpha

r x T = (m r^2 /2 ) ( a/r)

T = ma/2

putting in eqtn (i)

mg - ma/2 = ma

a = 2g /3 = 6.54 m/s^2 ...........ANs(c)

T = ma/2 = 0.30 x 6.54 /2 = 0.981 N .........Ans (B)

c) a = 6.54 m/s^2

using v^2 - u^2 = 2ad

v^2 - 0 = 2 x 6.54 x 0.5

v = 2.56 m/s

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