Hook's Law and Gravity Measurement

Questions and Answers

Match the following commercial gravimeters with their corresponding manufacturers:

LaCoste and Romberg = LaCoste and Romberg Texas Instruments = Texas Instruments Scintex = Scintex Worden Gravity meter = Texas Instruments

Match the following gravity observation techniques with their corresponding descriptions:

Spring-Based Gravimetry = Use elastic spring with a mass suspended to measure gravity Gravity Loop = Gravity observation corrected for static and dynamic drift, earth tide and calibration Optical Method = Method of recording (optical) and magnification (capacitative photo electric) Profile Method = One of the three methods used in field observation

Match the following gravity meters with their corresponding characteristics:

LaCoste and Romberg gravimeter = Accuracy: 0.01 mGal Scintex gravimeter = Resolution: 0.005 mGal Worden Gravity meter = Errors - Spring drift and temperature Texas Instruments gravimeter = Schematic-of-a-La-Coste-Romberg-gravimeter

Match the following gravity observation methods with their corresponding descriptions:

Profile method = One of the three methods used in field observation Star method = One of the three methods used in field observation Gravity Loop = Gravity observation corrected for static and dynamic drift, earth tide and calibration Hook's Law = 𝑚𝑔 = 𝑘(𝑙 − 𝑙𝑜 ) Signup and view all the answers

Match the following gravity measurement techniques with their corresponding requirements:

Spring-Based Gravimetry = Requires method of recording (optical) and magnification (capacitative photo electric) Gravity Loop = Should never exceed 72 hours Profile method = Corrected for static and dynamic drift, earth tide and calibration Optical Method = For small changes in 𝛿𝑔 (1 mGal) Signup and view all the answers

Match the following gravity observation errors with their corresponding descriptions:

Spring drift = Error in commercial gravimeters Temperature = Error in commercial gravimeters Static drift = Error corrected in gravity loop observation Dynamic drift = Error corrected in gravity loop observation Signup and view all the answers

Match the following gravity observation techniques with their descriptions:

Absolute observation = Observing directly the value of g at a point Relative measurement = Observing the difference in g between two points Pendulum = Free Fall Device Gravity Apparatus = Used to establish the value of gravity acceleration Signup and view all the answers

Match the following gravity units with their equivalent values:

1 Gal = 1 cms-2 = 10-2 ms-2 1 mgal = 10-3 gal = 10-5 ms-2 1 µgal = 10-6 gal = 10-8 ms-2 Gravity at equator = 978 Gal = 9.78 ms-2 Signup and view all the answers

Match the following gravity survey methods with their characteristics:

Potsdam system = Established in 1906, using reversible pendulums IGSN71 = Contains 1854 re-occupiable stations distributed worldwide Peninsular Malaysia Gravity Base Network = Total station = 33, Accuracy = ±0.005 mGal Gravity Apparatus = Used to establish the value of gravity acceleration Signup and view all the answers

Match the following gravity meters with their types of observation:

Pendulum = Absolute observation Free Fall Device = Absolute observation Commercial Gravimeters = Relative measurement Gravity Meters = Used to establish the value of gravity acceleration Signup and view all the answers

Match the following spring-based gravimetry techniques with their descriptions:

Absolute observation = Observing directly the value of g at a point Relative measurement = Observing the difference in g between two points Pendulum = Used in absolute observation Free Fall Device = Used in absolute observation Signup and view all the answers

Match the following gravity observation apparatus with their types of observation:

Match the following gravity survey networks with their characteristics:

IGSN71 = Contains 1854 re-occupiable stations distributed worldwide Peninsular Malaysia Gravity Base Network = Total station = 33, Accuracy = ±0.005 mGal Potsdam system = Established in 1906, using reversible pendulums Gravity Base Network = Used to establish the value of gravity acceleration Signup and view all the answers

Match the following gravity units with their equivalent values:

1 Gal = 1 cms-2 = 10-2 ms-2 1 mgal = 10-3 gal = 10-5 ms-2 1 µgal = 10-6 gal = 10-8 ms-2 Gravity at equator = 978 Gal = 9.78 ms-2 Signup and view all the answers

Match the following gravity observation techniques with their descriptions:

Pendulum = Measures gravity by swinging a pendulum and measuring its oscillation period. Falling Body Device = Measures gravity by observing the motion of a falling body over a distance of 1 or 2 meters. Reversible Pendulum = Removes the impact of vibration by swinging two pendulums on a fixed axis but in different directions. Rising and Falling Body = Improves accuracy by throwing a body upward and then allowing it to fall freely, passing the same level twice. Signup and view all the answers

Match the following terms with their definitions:

Gravimeter = A device that measures gravity. Gravity Meter = A device that measures gravity with high accuracy. Spring-Based Gravimetry = A method that uses a spring to measure gravity. Gravity Survey Methods = Techniques used to measure gravity in a specific area. Signup and view all the answers

Match the following limitations with their corresponding techniques:

Air friction and buoyancy = Pendulum Friction and temperature = Rising and Falling Body Difficulty in achieving ideal conditions = Simple Pendulum Costly and time-consuming = Falling Body Device Signup and view all the answers

Match the following formulas with their corresponding techniques:

$T = 2\pi \sqrt{\frac{l}{g}}$ = Simple Pendulum $g = \frac{2[ z1 - z2 (t1 - t3 ) - (z1 - z3 )(t1 - t2 )]}{(t1 - t2 )(t1 - t3 )(t2 - t3 )}$ = Falling Body Device $g = \frac{8 z2 - z1}{t4 - t1^2 - (t3 - t2 )^2}$ = Rising and Falling Body $T = \frac{4\pi }{\sqrt{g}} \frac{h1 + h2}{h1 + h2}$ = Reversible Pendulum Signup and view all the answers

Match the following advantages with their corresponding techniques:

Removes the impact of vibration = Reversible Pendulum Improves accuracy = Rising and Falling Body Measures gravity with high accuracy = Gravity Meter Uses a spring to measure gravity = Spring-Based Gravimetry Signup and view all the answers

Match the following disadvantages with their corresponding techniques:

Bulky equipment = Pendulum and Falling Body Device Costly = Gravity Meter Time-consuming = Falling Body Device Difficult to achieve ideal conditions = Simple Pendulum Signup and view all the answers

Match the following terms with their corresponding descriptions:

Absolute Gravimeter = A device that measures gravity with high accuracy. Relative Gravimeter = A device that measures gravity relative to a standard value. Gravity Survey Methods = Techniques used to measure gravity in a specific area. Commercial Gravimeters = Devices that measure gravity for commercial purposes. Signup and view all the answers

Match the following techniques with their corresponding principles:

Pendulum = Dynamic method Falling Body Device = Dynamic method Reversible Pendulum = Dynamic method Gravimeter = Static method Signup and view all the answers

Match the following errors with their corresponding techniques:

Air friction and buoyancy = Pendulum Friction and temperature = Rising and Falling Body Vibration on the foundation = Pendulum Molecule of air are absorbed on the shark of the pendulum = Pendulum Signup and view all the answers

Match the following techniques with their corresponding accuracy:

Rising and Falling Body = 0.006 mGal Falling Body Device = 0.01 mGal Pendulum = 0.1 mGal Gravimeter = 0.001 mGal Signup and view all the answers

Study Notes

Gravity Observation Technique

Gravity observation is used to establish the value of gravity acceleration at a desired point, either through absolute or relative measurements.

Measurement Techniques

Spring with a mass suspended: uses Hook's Law (mg = k(l - lo)) to measure gravity acceleration.
Gravity loop: a technique that corrects for static and dynamic drift, earth tide, and calibration.
There are three methods: Profile method, Star method, and Gravimeters – Absolute and Relative observation.

Commercial Gravimeters

Examples: LaCoste and Romberg, Texas Instruments (Worden Gravity meter), and Scintex.
Accuracy: 0.01 mGal, Resolution: 0.005 mGal, Errors: Spring drift and temperature.

Pendulum

A simple pendulum uses a dimensionless material, suspended on a perfectly flexible, unstretchable, massless string of length L.
The pendulum's oscillation period (T) is measured to calculate gravity acceleration (g).
Simple theory, but difficult to implement due to the need for an ideal pendulum and ideal length, with timing accuracy.

Errors in Pendulum Method

Air friction dampens the pendulum swing and causes buoyancy effects.
Molecules of air are absorbed on the shaft of the pendulum, changing the length.
Vibration on the foundation affects the pendulum's rest.

Reversible Pendulum

Developed by Kater in 1818.
Uses two pendulums on a fixed axis, but in different directions, with the same oscillation period.
Removes the impact of vibration.

Falling Body Device

Observes the motion of a falling body over a distance of 1 or 2 meters.
Calculates gravity acceleration (g) by eliminating z0 and v0 from three position equations.

Rising and Falling Body

An improvement over the falling body method.
Body is thrown upward and then falls freely, passing the same level twice.
Calculates gravity acceleration (g) by eliminating z0 and v0 from four equations.

Gravity Meter (Gravimeter)

Uses a static method, measuring gravity acceleration directly.
Examples: GSS611 Physical Geodesy.

SI Unit for Gravity

Unit for gravity is Gal or cms-2, named after Galileo Galilee.
1 Gal = 1 cms-2 = 10-2 ms-2, 1 mgal = 10-3 gal, 1 µgal = 10-6 cms-2 = 10-8 ms-2.
Gravity at the equator ≈ 978 Gal = 9.78 ms-2 = 978,000 mgal.

Gravity Datum

Earliest gravity datum: Potsdam system (Germany, 1906), using reversible pendulums to establish absolute gravity value.
International Gravity Standardization Net 1971 (IGSN71): replaced Potsdam system, contains 1854 re-occupiable stations worldwide, with an accuracy of ±0.000017gal.
Peninsular Malaysia Gravity Base Network: 33 stations, accuracy of ±0.005 mGal, with 4 IGSN stations (KL, Penang, Malacca, Singapore) with an accuracy of 0.05 mGal — 0.1 mGal.

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Description

This quiz covers the application of Hook's Law in measuring gravity, including the relationship between spring elasticity and gravity force.

Hook's Law and Gravity Measurement

Questions and Answers

Match the following commercial gravimeters with their corresponding manufacturers:

Match the following gravity observation techniques with their corresponding descriptions:

Match the following gravity meters with their corresponding characteristics:

Match the following gravity observation methods with their corresponding descriptions:

Match the following gravity measurement techniques with their corresponding requirements:

Match the following gravity observation errors with their corresponding descriptions:

Match the following gravity observation techniques with their descriptions:

Match the following gravity units with their equivalent values:

Match the following gravity survey methods with their characteristics:

Match the following gravity meters with their types of observation:

Match the following spring-based gravimetry techniques with their descriptions:

Match the following gravity observation apparatus with their types of observation:

Match the following gravity survey networks with their characteristics:

Match the following gravity units with their equivalent values:

Match the following gravity observation techniques with their descriptions:

Match the following terms with their definitions:

Match the following limitations with their corresponding techniques:

Match the following formulas with their corresponding techniques:

Match the following advantages with their corresponding techniques:

Match the following disadvantages with their corresponding techniques:

Match the following terms with their corresponding descriptions:

Match the following techniques with their corresponding principles:

Match the following errors with their corresponding techniques:

Match the following techniques with their corresponding accuracy:

Study Notes

Gravity Observation Technique

Measurement Techniques

Commercial Gravimeters

Pendulum

Errors in Pendulum Method

Reversible Pendulum

Falling Body Device

Rising and Falling Body

Gravity Meter (Gravimeter)

SI Unit for Gravity

Gravity Datum

Studying That Suits You

Description

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