Question

A *m _{1}* = 16.6 kg mass and a

The answer is not 2.42 m/s. Thanks!

Answer #1

Since m1 > m2, it will accelerate downwards

m1a = m1g - T1------1

m2a = T2 - m2g--------2

For the Pulley, net torque

Tnet = T - T' = T1r - T2r = r(T1 - T2) = I.alpha = (1/2)MR^2.(a/R)

=> r(T1 - T2) = (1/2)MR^2.(a/R)

=> T1 - T2 = (1/2)Ma---------3

From 1, 2 and 3,

m1g - m1a - m2g - m2a = (1/2)Ma

16.6*9.81 - 16.6*a - 10.1*9.81 - 10.1*a = (1/2)(2.6)a

a = 2.28 m/s^2

Keep in mind that both boxes are accelerating, so their closing
acceleration will be twice the value of a or 4.56 m/s^2

vf² = vi² + 2ad

vf² = (0 m/s)² + 2(4.56 m/s²)(3.30 m)

vf = 5.48 m/s

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