Determine the acceleration of gravity on the surface of Mars, provided that there a mathematical

| August 6, 2021 | education

Determine the acceleration of gravity on the surface of Mars, provided that there a mathematical pendulum 50 cm long would make 40 oscillations in 80 seconds.

Answer: 4.93 m / s ^ 2.
Solution: first you need to find the oscillation period of the mathematical pendulum according to the formula: T = t / N, where T is the period, t is the oscillation time, N is the number of oscillations, substituting the values we get: T = t / N = 80/40 = 2 s. Further, from the formula: T = 2 * n * (l / g) ^ 1/2, where l is the length of the mat. pendulum, g is the acceleration of gravity, we express g:
T = 2 * n * (l / g) ^ 1/2
T * (g) ^ 1/2 = 2 * n * (l) ^ 1/2
(g) ^ 1/2 = 2 * n * (l) ^ 1/2 / T
g = 4 * n ^ 2 * l / T ^ 2
l = 0.5 m, we substitute the values in the resulting formula: g = 4 * n ^ 2 * l / T ^ 2 = 4 * (3.14) ^ 2 * 0.5 / 2 ^ 2 = 4.93 m / c ^ 2.



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