1. A simple Atwood\'s machine uses two masses, m 1 and m 2 . Starting from rest,

Question

1. A simple Atwood's machine uses two masses, m1 and m2. Starting from rest, the speed of the two masses is 5.0 m/s at the end of 10.0 s. At that instant, the kinetic energy of the system is 60 J and each mass has moved a distance of 25.0 m. Determine the values of m1 and m2.
m1 = ?  kg
m2 = ? kg

2. A simple Atwood's machine uses two masses, m1 and m2. Starting from rest, the speed of the two masses is 6.0 m/s at the end of 7.0 s. At that instant, the kinetic energy of the system is 50 J and each mass has moved a distance of 21.0 m. Determine the values of m1 and m2.
m1 = ? kg
m2 = ? kg

Explanation / Answer

For a simple Atwood's machine,

a = [m1 - m2/(m1 + m2)]g

a = v/t = 5/10 = 0.5 m/s^2

m1 - m2 = a (m1 + m2)/g (1)

KE = 1/2 (m1 + m2) v^2 = 60

m1 + m2 = 120/5^2 = 4.8

m1 - m2 = 0.5 x 4.8/9.8 = 0.225

m1 + m2 + m1 - m2 = 4.8 + 0.225

2m1 = 5.025 => m1 = 2.513 kg

2.513 + m2 = 4.8 => m2 = 4.8 - 2.513 = 2.287 kg

Hence, m1 = 2.513 kg and m2 = 2.287 kg

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