An Atwood machine consists of two masses ?1 and ?2 (with ?1 > ?2) attached to the ends of a light string that passes over a light, frictionless pulley. When the masses are released, the mass ?1 is easily shown to accelerate down with an acceleration ? = ? (?1 − ?2)/m1+m2 Suppose that ?1 and ?2 are measured as ?1 = 100 ± 1 ???? and ?2 = 50 ± 1 ????. Derive a formula of the uncertainty in the expected acceleration in terms of the masses and their uncertainties, and then calculate ?? for the given numbers.

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5. An Atwood machine consists of two masses ?1 and ?2 (with ?1 > ?2) attached to the
ends of a light string that passes over a light, frictionless pulley. When the masses are released,
the mass ?1 is easily shown to accelerate down with an acceleration
? = ? (?1 − ?2)/m1+m2
Suppose that ?1 and ?2 are measured as ?1 = 100 ± 1 ???? and ?2 = 50 ± 1 ????.
Derive a formula of the uncertainty in the expected acceleration in terms of the masses and
their uncertainties, and then calculate ?? for the given numbers.
 
 
5. 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
M₁ M₂
m₁ + m₂
a = g
Suppose that m₁ and m₂ are measured as m₁ = 100 ± 1 gram and m₂ = 50 ± 1 gram.
Derive a formula of the uncertainty in the expected acceleration in terms of the masses and
their uncertainties, and then calculate da for the given numbers.
Transcribed Image Text:5. 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 M₁ M₂ m₁ + m₂ a = g Suppose that m₁ and m₂ are measured as m₁ = 100 ± 1 gram and m₂ = 50 ± 1 gram. Derive a formula of the uncertainty in the expected acceleration in terms of the masses and their uncertainties, and then calculate da for the given numbers.
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