An Atwood machine is made with masses M1 = 100 g, M2 = 120 g, and pulley mass of

Question

An Atwood machine is made with masses M1 = 100 g, M2 = 120 g, and pulley mass of 100 g. What is the percent error in acceleration (relative to the corrected formula) calculated by neglecting the pulley mass versus incorporating the pulley mass?

Explanation / Answer

without taking the mass of the pulley into account, your expression for acceleration is a = (m2-m1)g/(m2+m1) taking the mass of the pulley into account, our three equations become: for mass m2, m2>m1: T2 - m2g = - m2a (the negative sign means m2 is accelerating down) for mass m1: T1 - m1g = m1a for the pulley torque = (T2-T1)R = I alpha I = 1/2 MR^2 where M, R are the mass and radius of the pulley, and 1/2 MR^2 is the moment of inertia for a solid disk, alpha is the angular accel = a/R therefore the torque equation becomes (T2-T1)R = 1/2 MR^2(a/R) T2-T1= 1/2 Ma combine these equations to get your expression for acceleration: a=(m2-m1)g/(m1+m2+1/2M) the two accelerations are easily calculated: a(neglecting pulley) = 0.89m/s/s a(with pulley) = 0.61m/s/s percent error = 31.3%

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