In an Atwood\'s machine, one block has a mass of 874.0 g, and the other a mass o
ID: 2161611 • Letter: I
Question
In an Atwood's machine, one block has a mass of 874.0 g, and the other a mass of 1014.0 g. The pulley, which is mounted in horizontal frictionless bearings, has a radius of 8.70 cm. When released from rest, the heavier block is observed to fall 95.0 cm in 2.23 s (without the string slipping on the pulley).1)What is the magnitude of the acceleration of the 874.0-g block?
2)What is the magnitude of the acceleration of the 1014.0-g block?
3)What is the magnitude of the tension in the part of the cord that supports the 874.0-g block?
4)What is the magnitude of the tension in the part of the cord that supports the 1014.0-g block?
5)What is the magnitude of the angular acceleration of the pulley?
6)What is the rotational inertia of the pulley?
7)What is the change in the potential energy of the system after 2.23 s?
Explanation / Answer
m = 0.874 kg, M = 1.014 kg, r = 8.70 cm, h = 0.95 m, t = 2.23 s
1)What is the magnitude of the acceleration of the 874.0-g block?
a = 2h/t2 = 0.382 m/s2
2)What is the magnitude of the acceleration of the 1014.0-g block?
a = 0.382 m/s2
3)What is the magnitude of the tension in the part of the cord that supports the 874.0-g block?
T1 = m(g + a) = 8.91 N
4)What is the magnitude of the tension in the part of the cord that supports the 1014.0-g block?
T2 = M(g - a) = 9.56 N
5)What is the magnitude of the angular acceleration of the pulley?
= a/r = 4.39 rad/s2
6)What is the rotational inertia of the pulley?
I = (T2 - T1)r/ = 0.0129 kgm2
7)What is the change in the potential energy of the system after 2.23 s?
mgh - Mgh = (m - M)gh = -1.30 J
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