In an Atwood\'s machine, one block has a mass of 816.0 g, and the other a mass o

Question

In an Atwood's machine, one block has a mass of 816.0 g, and the other a mass of 1006.0 g. The pulley, which is mounted in horizontal frictionless bearings, has a radius of 3.30 cm. When released from rest, the heavier block is observed to fall 92.6 cm in 3.67 s (without the string slipping on the pulley). The pulley has mass so the tensions will not be equal.

What is the magnitude of the acceleration of the 816.0-g block?

What is the magnitude of the acceleration of the 1006.0-g block?

What is the magnitude of the tension in the part of the cord that supports the 816.0-g block?

What is the magnitude of the tension in the part of the cord that supports the 1006.0-g block?

What is the magnitude of the angular acceleration of the pulley?

What is the rotational inertia of the pulley?

What is the change in the potential energy of the system after 3.67 s?

Explanation / Answer

Applying d = v0 t + a t^2 / 2

0.926 = 0 + a (3.67^2) / 2

a = 0.1375 m/s^2

acceleration of both 816g and 1006g = 0.14 m/s^2 ....Ans

T - 0.816 g = 0.816 a

T = 0.816 (9.81 + 0.14) = 8.117 N ......Ans

1.006g - T = 1.006 a

T = 9.731 N ........Ans

alpha = a / r = 0.1375 / 0.033 = 4.167 rad/s^2 ......Ans

torque = I alpha

0.033 ( 9.731 - 8.117) = I (4.167)

I = 0.01278 kg m^2 .........Ans

v = a t = 0.505 m/s

change in PE = - (0.816 + 1.006)(0.505^2) /2

= -0.232 J ......Ans

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