Two metal disks, one with radius R 1 = 2.60 cmand mass M 1 = 0.850 kg and the ot

Question

Two metal disks, one with radius R1 = 2.60 cmand mass M1 = 0.850 kg and the other with radius R2 = 4.95 cm and mass M2 = 1.65 kg , are welded together and mounted on a frictionless axis through their common center. A light string is wrapped around the edge of the smaller disk and a 1.45 kg block is suspended from the free end of the string.

a) What is the magnitude of the downward acceleration of the block after it is released?(Take the free fall acceleration to be 9.80m/s2.)

b)Repeat the calculation of part (a), this time with the string wrapped around the edge of the larger disk.(Take the free fall acceleration to be 9.80m/s2.)

Explanation / Answer

I=(0.850*0.0261^2+1.65*0.0495^2)/2

0.00232 kg m^2

A FBD of the hanging mass
1.45*9.8-T=1.45*a

where T is the tension

A FBD of the disks
T*0.0261=0.00232*a/0.0261

combine and solve for a
T=4*a

a=1.45*9.8/5.45
2.607 m/s^2

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