Assuming that the uncertainty in mass is negligible, and the uncertainty in velocity is 5 %, what is the uncertainty in the momentum of your two-cart system?

 Δp = 0.05 p

Explanation:

The moment is

      p = m v

The uncertainty of the moment is

       Δp = dp/dm Δm + dp/dv Δv

Like the uncertainty in the mass is zero

       Δm = 0

       ΔP = m Δv

We divide for the moment

       Δp / p = Δv / v

  They do not indicate that Δv / v = 0.05

       Δp / p = 0.05

       Δp = 0.05 p

In the case of a system consisting of two cars

      p = m₁ v₁ + m₂ v₂

     Δp = dp / dv₁ Δv₁ + dp / dv₂ Δv₂

     Δp = m₁ Δv₁ + m₂ Δv₂

     Δv₁ / v₁ = 0.05

     Δv₁ = 0.05 v₁

     Δv₂ / v₂ = 0.05

     Δv₂ = 0.05 v₂

We replace

       Δp = m₁ 0.05 v₁ + m₂ 0.05 v₂

       Δp = 0.05 p

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