The period t of a simple pendulum is given by t = 2π formula887. mml, where l is the length of the pendulum and g is the acceleration due to gravity. thus if l and t are measured, we can estimate g with g = 4π2l/t2. assume that the period is known to be t = 1.49 s with negligible uncertainty and that l is measured to be 0.559 ± 0.005 m. estimate g, and find the uncertainty in the estimate. note: when doing calculations, use pi = 3.1416.

Question

Mathematics

Quinn Saunders

1 July, 12:26

The period t of a simple pendulum is given by t = 2π formula887. mml, where l is the length of the pendulum and g is the acceleration due to gravity. thus if l and t are measured, we can estimate g with g = 4π2l/t2. assume that the period is known to be t = 1.49 s with negligible uncertainty and that l is measured to be 0.559 ± 0.005 m. estimate g, and find the uncertainty in the estimate. note: when doing calculations, use pi = 3.1416.

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Valeria Dougherty · Answer 1

Filling in the given numbers, you have

... g = 4 (3.1416/1.49) ²·0.559 ≈ 9.9403

The error is proportional to the length, so is

... ±∆g = ± (0.005/0.559) g = ±0.0889

The estimate for the value of g is 9.9403 ± 0.0889 m/s².