A Modified Atwoods Machine consists of two masses, m1 = 2 kg and m2 = 3 kg which

Question

A Modified Atwoods Machine consists of two masses, m1 = 2 kg and m2 = 3 kg which are connected by a massless inelastic cord that passes over a pulley, (see figure). If the pulley is a uniform disk with radius 0.1 m and mass M = 1 kg, determine the acceleration of the system. Assume that the rope doesn't slip on the pulley. Note that since the pulley is not massless, the tensions in the two sides of the rope may not be the same

A Modified Atwood½s Machine consists of two masses, m1 = 2 kg and m2 = 3 kg which are connected by a massless inelastic cord that passes over a pulley, (see figure). If the pulley is a uniform disk with radius 0.1 m and mass M = 1 kg, determine the acceleration of the system. Assume that the rope doesn't slip on the pulley. Note that since the pulley is not massless, the tensions in the two sides of the rope may not be the same

Explanation / Answer

I=0.5mr2=0.005kgm2

Writing equation of motion for blocks,

3g-T2=3a

T2+3a=29.4 (1)

T1-2g=2a

T1-2a=19.6 (2)

For pulley,

(T2-T1)r=I

(T2-T1)r=Ia/r

(T2-T1)=Ia/r2

T2-T1=0.5a (3)

Solving (1) (2) and (3),

T2=24.1N

T1=23.2N

a=1.782m/s2

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