Use dimensional analysis to show that increase in g due to lead

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SUMMARY

The discussion focuses on using dimensional analysis to demonstrate that the increase in gravitational field strength (\(\Delta g\)) at a clock due to a layer of lead is proportional to the product of the gravitational constant (G), the thickness of the lead (d), and its density (\(\rho\)). The equation established is \(\Delta g = kGd\rho\), where k is a proportionality constant. Participants highlighted the importance of correctly identifying the units for each variable, particularly the thickness (d), to ensure dimensional consistency.

PREREQUISITES
  • Understanding of dimensional analysis in physics
  • Familiarity with gravitational concepts and the gravitational constant (G)
  • Knowledge of units of measurement in physics, particularly for mass, length, and time
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the principles of dimensional analysis in greater depth
  • Explore the implications of gravitational fields in different materials
  • Learn about the gravitational constant (G) and its applications in physics
  • Investigate how density and thickness affect gravitational interactions
USEFUL FOR

Students in physics, particularly those studying mechanics and gravitational theory, as well as educators looking to enhance their understanding of dimensional analysis and its applications in real-world scenarios.

cloudone
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Homework Statement


A clock is placed on a floor covered with lead density [tex]\rho[/tex] and thickness d. Use dimensional analysis to show that increase in gravitational field strength at the clock dueo to the layer of lead is proportional to [tex]Gd\rho[/tex]

Homework Equations


The Attempt at a Solution


to show that [tex]\Delta g = kGd\rho[/tex]

units of [tex]\Delta g = m s^{-2}[/tex]

units of [tex]Gd\rho = m^{3}kg^{-1}s^{-2}kgm^{-3}[/tex]

I don't get why they're not the same.
 
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cloudone said:

Homework Statement


A clock is placed on a floor covered with lead density [tex]\rho[/tex] and thickness d. Use dimensional analysis to show that increase in gravitational field strength at the clock dueo to the layer of lead is proportional to [tex]Gd\rho[/tex]


Homework Equations





The Attempt at a Solution


to show that [tex]\Delta g = kGd\rho[/tex]

units of [tex]\Delta g = m s^{-2}[/tex]

units of [tex]Gd\rho = m^{3}kg^{-1}s^{-2}kgm^{-3}[/tex]

I don't get why they're not the same.

You forgot to include the units for d, the thickness.
 
Stonebridge said:
You forgot to include the units for d, the thickness.

argh, thanks. I just realized that. I've been thinking dp as differential of p
 

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