An `Atwood machine\' can be used to accurately measure g on Earth or on another

Question

An `Atwood machine' can be used to accurately measure g on Earth or on another planet. Suppose the two masses are m1 = 38 kg and m2 = 32 kg. The pulley is a cylinder of mass M = 64 kg and radius 31 cm. The string passes over this pulley without slipping, but the pulley is on frictionless bearings. When released from rest, the heavier mass moves down 146.3 cm in 1.3 s. What is g at this location?

An `Atwood machine' can be used to accurately measure g on Earth or on another planet. Suppose the two masses are m1 = 38 kg and m2 = 32 kg. The pulley is a cylinder of mass M = 64 kg and radius 31 cm. The string passes over this pulley without slipping, but the pulley is on frictionless bearings. When released from rest, the heavier mass moves down 146.3 cm in 1.3 s. What is g at this location?

Explanation / Answer

s = u*t + 0.5*a*t^2

1.463 = 0 + 0.5*a*1.3^2

a = 1.731 m/s^2


Torque Q = I*a/R = (T1-T2)*R


I = 0.5*M*R^2


(T1-T2)*R = 0.5*M*R^2*a/R

T1 - T2 = 0.5*M*a.........(1)

m1 g -T1 = m1 a........(2)

T2 - m2g = m2 a...........(3)

2+3

m1g - (T1 - T2) - m2g = a*(m1+m2)


m1g - 0.5*M*a - m2 g = a(m1+m2)

g*(m1-m2) = a*[(m1+m2)+0.5*M ]

g = a*[(m1+m2)+0.5*M ]/(m1-m2)

g = ((1.731*(38+32)+(0.5*64))/(38-32)) = 29.427 m/s^2

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