Question

An Atwood machine consists of two masses m1 and m2 (with m1 > m2 ) attached to the ends of a light string that passes over a light, frictionless pulley. When the masses are released, the mass m1 is easily shown to accelerate down with an acceleration a = g*(m1+m2)/)m1−m2 Suppose that m and are measured as m1 = 100 +- 1 gram and m2 = 50 +- 1 gram. Derive a formula of uncertainty in the expected acceleration in terms of the masses and their uncertainties, then calculate the error of a for the given numbers.

Answer 1

acceleration ,

a = (m1 – m2) (mı + m2) 7

uncertainty in m1 = Δm1

uncertainty in m2 = Δm2

Uncertainty in acceleration is given by

да Да = да * Дm1 + — | * Дт. | дм2 |дті

Aa= 2m2 g (mi + m2) ) * Ami + 2m 9 ) * Amz (mı + m2))

substituting the values,

m1 = 100 +- 1 gram

m2 = 50 +- 1 gram

2(50) 9 Aa= . 12(100) g *1+1 (150) 150

Aa

taking g = 9.8 m/s²

Aa 0.13 m/s?