Two metal disks, one with radiusR1= 2.44cmand massM1= 0.750kg and the other with

Question

Two metal disks, one with radiusR1= 2.44cmand massM1= 0.750kg and the other with radiusR2 = 4.90cmand mass M2 = 1.69kg, are welded together and mounted on a frictionless axis through their common center.(Figure 1).A light string is wrapped around the edge of the smaller disk, and a 1.50-kg block, suspended from the free end of the string. If the block is released from rest at a distance .05mabove the floor, what is its speed just before it strikes the floor? Repeat the calculation of part B, this time with the string wrapped around the edge of the larger disk.

Explanation / Answer

I = 1/2 m1r2^2 + 1/2 m2r2^2

= 2.25*10^-3 kg m^2

Speed of block = w*r1 = w*0.0244

PE = rotational K.E of discs + linear K.E of block

1.5*9.8*2.05 = 1/2 * 2.25*10^-3 * w^2 + 1/2 * 1.5 * (0.0244w)^2

w = 138.47 rad/s

speed = 138.47 * 0.0244 = 3.38 m/s

(b)

Speed of block = w*r1 = w*0.049

PE = rotational K.E of discs + linear K.E of block

1.5*9.8*2.05 = 1/2 * 2.25*10^-3 * w^2 + 1/2 * 1.5 * (0.49w)^2

w = 101.49 rad/s

speed = 101.49*0.049 = 4.97 m/s

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