An Atwood machine consists of two masses, m A = 64 kg and m B = 74 kg , connecte

Question

An Atwood machine consists of two masses, mA = 64 kg and mB = 74 kg , connected by a massless inelastic cord that passes over a pulley free to rotate (Figure 1) . The pulley is a solid cylinder of radius R = 0.44 m and mass 6.0 kg . [Hint: The tensions FTA and FTB are not equal.]

Part A

Determine the acceleration of each mass.

Express your answer to two significant figures and include the appropriate units.

Part B

What % error would be made if the moment of inertia of the pulley is ignored?

Express your answer using two significant figures.

Explanation / Answer

A) let a is the acceleration of blocks

TA = mA*g + mA*a

TB = mB*g - mB*a

Net torque actin on cyllinder,

Tnet = I*alfa

(TB - TA)*R = 0.5*m*R^2*(a/R)

TB - TA = 0.5*m*a

mB*g - mB*a - mA*g - mA*a = 0.5*m*a

(mB - mA)*g = a*(0.5*m + mA +mB)

==> a = (mB - mA)*g/(0.5*m + mA +mB)

= (74 - 64)*9.8/(0.5*6 + 64 + 74)

= 0.695 m/s^2

B) when we neglect moment of inertia of pulley, a' = g*(mB - mA)/(mA+MB)

= 9.8*(74 - 64)/(64 + 74)

= 0.71 m/s^2

a'/a = 0.71/0.69

a' = a*1.0218

= a + 0.0218*a

= a + 2.18% of a

so, error 2.18%

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