The earth's free-fall acceleration varies from 9.78 m / s^2...

The earth's free-fall acceleration varies from $9.78 \mathrm{m} / \mathrm{s}^{2}$ at the $64 .$ equator to $9.83 \mathrm{m} / \mathrm{s}^{2}$ at the poles, both because the earth is rotating and it's not a perfect sphere. A pendulum whose length is precisely $1.000 \mathrm{m}$ can be used to measure $g .$ Such a device is called a gravimeter a. How long do 100 oscillations take at the equator? b. How long do 100 oscillations take at the north pole? c. Is the difference between your answers to parts a and b measurable? What kind of instrument could you use to measure the difference? d. Suppose you take your gravimeter to the top of a high mountain peak near the equator. There you find that 100 oscillations take $201.0 \mathrm{s}$. What is $g$ on the mountain top?

The earth's free-fall acceleration varies from $9.78 \mathrm{m} / \mathrm{s}^{2}$ at the $64 .$ equator to $9.83 \mathrm{m} / \mathrm{s}^{2}$ at the poles, both because the earth is rotating and it's not a perfect sphere. A pendulum whose length is precisely $1.000 \mathrm{m}$ can be used to measure $g .$ Such a device is called a gravimeter
a. How long do 100 oscillations take at the equator?
b. How long do 100 oscillations take at the north pole?
c. Is the difference between your answers to parts a and b measurable? What kind of instrument could you use to measure the difference?
d. Suppose you take your gravimeter to the top of a high mountain peak near the equator. There you find that 100 oscillations take $201.0 \mathrm{s}$. What is $g$ on the mountain top?

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Key Concepts

Gravitational Acceleration

This is the measure of the force per unit mass exerted by the Earth’s gravity. It varies with location due to factors such as altitude, latitude, and the Earth's rotation and oblateness, affecting how objects experience free-fall.

Pendulum Motion

A simple pendulum exhibits periodic motion, where its period (the time for one complete oscillation) is determined by its length and the local gravitational acceleration by the formula T = 2??(L/g). This relationship is a fundamental aspect of simple harmonic motion in mechanics.

Gravimetry

Gravimetry is the measurement of the local gravitational acceleration. Instruments like the pendulum gravimeter use the predictable oscillatory behavior of pendulums to infer the value of g at different locations, making it a useful tool for both scientific and geophysical studies.

Measurement Precision

Precision in measurement refers to the ability of an instrument to detect small differences or changes in a quantity. In gravimetry, high precision is essential for discerning subtle variations in gravitational acceleration due to factors like geographical location or altitude.

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