Abstract

The experiment demonstrates the approximate derivation of the gravitational force (g), 100m above Earth’s surface. The gravitational force ($g$) on Earth varies with location. Although, the nominal “average” value on Earth’s surface equates to 9.807 m/s² for all practical intents & purposes [1]. The following experiment uses a miscellanea of crude household equipments & measurement devices to derive the $\text{gravitational force (g)} \approx \text{10.02 m/s}^2$.The margin of error is anticipated, bound by the crudeness of the apparatus.

Setup

An object is released from a measured height of $\text {d = 1.5}\pm\text{0.02m}$. The time ($t$) is measured as the time from the instant of release to the instant when the object touches the ground. The measurement is carried out by a sophisticated device with a voltage-controlled crystal oscillator (a smartphone). The time is averaged across 10 trials, to offset much of the human-induced errors.

Experiment

Untitled

$$ \text{Mean t(s) = 0.547} $$

Measurement

<aside> ⚙ Variables

$$ \begin{aligned} d &= 1.5±0.02m \\ t0 &= 0s \\ u &= 0m \\ t &= 0.547s \\ g &= a = ? \end{aligned} $$

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We can use the Second Equation of Motion to calculate the acceleration $a$ of the object, displaced by the distance $d$.[2]

$$ \begin{equation} \begin{split} d&=ut+\frac{1}{2}at^2\\1.5&=0(0.547)+\frac{1}{2}a(0.547)^2 \\\therefore \bold a &\bold{\text{ }\approx\text{ }10.02 \text { } m/s^2} \end{split} \end{equation} $$

Conclusion

As derived from the experiment, we can show $\text{gravitational force (g)} \approx \text{10.02 m/s}^2$ (within margin of error of the “actual” value of $g$). Owing to the replicability of the fact; from a simple setup as such, we can derive the gravitational force ($g$) with adequate enough precision.

References

  1. https://en.wikipedia.org/wiki/Gravity_of_Earth
  2. https://byjus.com/physics/derivation-of-equation-of-motion/#derivation-of-second-equation-of-motion