Hook's Law and Gravity Measurement
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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:

<p>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 )</p> Signup and view all the answers

Match the following gravity measurement techniques with their corresponding requirements:

<p>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)</p> Signup and view all the answers

Match the following gravity observation errors with their corresponding descriptions:

<p>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</p> Signup and view all the answers

Match the following gravity observation techniques with their descriptions:

<p>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</p> Signup and view all the answers

Match the following gravity units with their equivalent values:

<p>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</p> Signup and view all the answers

Match the following gravity survey methods with their characteristics:

<p>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</p> Signup and view all the answers

Match the following gravity meters with their types of observation:

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

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

<p>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</p> Signup and view all the answers

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

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

Match the following gravity survey networks with their characteristics:

<p>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</p> Signup and view all the answers

Match the following gravity units with their equivalent values:

<p>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</p> Signup and view all the answers

Match the following gravity observation techniques with their descriptions:

<p>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.</p> Signup and view all the answers

Match the following terms with their definitions:

<p>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.</p> Signup and view all the answers

Match the following limitations with their corresponding techniques:

<p>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</p> Signup and view all the answers

Match the following formulas with their corresponding techniques:

<p>$T = 2\pi \sqrt{\frac{l}{g}}$ = 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</p> Signup and view all the answers

Match the following advantages with their corresponding techniques:

<p>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</p> Signup and view all the answers

Match the following disadvantages with their corresponding techniques:

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

Match the following terms with their corresponding descriptions:

<p>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.</p> Signup and view all the answers

Match the following techniques with their corresponding principles:

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

Match the following errors with their corresponding techniques:

<p>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</p> Signup and view all the answers

Match the following techniques with their corresponding accuracy:

<p>Rising and Falling Body = 0.006 mGal Falling Body Device = 0.01 mGal Pendulum = 0.1 mGal Gravimeter = 0.001 mGal</p> 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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This quiz covers the application of Hook's Law in measuring gravity, including the relationship between spring elasticity and gravity force.

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