The mass of the upper magnet array is 59.87 g ± 0.05g, and the height 𝒉 𝟏 of the magnetic barrier is 1.3 cm± 0.05cm. The height 𝒉 𝟐 at which the upper array reliably overcomes the magnetic force barrier is 5.1 cm ± 0.05cm. The difference is 3.8 cm ± 0.1 cm and corresponds to height 𝒉. The acceleration due to gravity is 9.8 m/s 2 . Converting to SI units and plugging into Formula (1) yields a potential energy 𝚬 𝒑 = 2.2 x 10 -2 J ± 3.2 x 10 -5 J to overcome the magnetic potential barrier. Thus, per Formula (3), a velocity of at least 𝒗 = 0.16 m/s ± 5.1 x 10 -3 m/s is required to overcome the magnetic potential barrier.