10.63 ... Two metal disks, one with radius R 1 = 2.50 cm and mass M 1 = 0.80 kg

Question

10.63 ... Two metal disks, one with radius R1 = 2.50 cm and mass M1 = 0.80 kg and the other with radius R2 = 5.00 cm and mass M2 = 1.60 kg, are welded together and mounted on a fric- tionless axis through their common center, as in Problem 9.77. (a) A light string is wrapped around the edge of the smaller disk, and a 1.50-kg block is suspended from the free end of the string. What is the magnitude of the downward acceleration of the block after it is released? (b) Repeat the calculation of part (a), this time with the string wrapped around the edge of the larger disk. In which case is the acceleration of the block greater? Does your answer make sense?

Explanation / Answer

here,

M1 = 0.8 kg

R1= 0.025 m

M2 = 1.6 kg

R2 = 0.05 m

let the tension in the string be T

a)

let the accelration be a

for the block ,

m * g - T = m * a

1.5 * 9.8 - T = 1.5 * a ....(1)

and

I * alpha = T * R1

( 0.5 * m1 * R1^2 + 0.5 m2*R2^2) * a / R1 = T * R1

0.5 * ( 0.8*0.025^2 + 1.6 *0.05^2) * a = T * 0.025^2 ....(2)

from (1) and (2)

a = 2.88 m/s^2

the accelration of the block is 2.88 m/s^2

b)

let the accelration be a

for the block ,

m * g - T = m * a

1.5 * 9.8 - T = 1.5 * a ....(1)

and

I * alpha = T * R2

( 0.5 * m1 * R1^2 + 0.5 m2*R2^2) * a / R2 = T * R2

0.5 * ( 0.8*0.025^2 + 1.6 *0.05^2) * a = T * 0.05^2 ....(2)

from (1) and (2)

a = 6.125 m/s^2

the accelration of the block is 6.125 m/s^2

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