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

In summary, when using dimensional analysis to show the increase in gravitational field strength at a clock due to a layer of lead with density \rho and thickness d, the resulting equation is \Delta g = kGd\rho, where the units for \Delta g are m s^{-2} and the units for Gd\rho are m^{3}kg^{-1}s^{-2}kgm^{-3}. It is important to remember to include the units for all variables, including d, in order for the equation to be accurate.
  • #1
cloudone
5
0

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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  • #2
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.
 
  • #3
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
 

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

1. How does dimensional analysis show the increase in g due to lead?

Dimensional analysis is a mathematical tool used to convert between different units of measurement. By using this method, we can show that an increase in the mass of an object, such as lead, will result in a corresponding increase in the force of gravity acting on that object.

2. What is the equation used in dimensional analysis to show the increase in g due to lead?

The equation used in dimensional analysis for this scenario is F = mg, where F represents the force of gravity, m represents the mass of the object, and g represents the acceleration due to gravity.

3. How does the mass of lead affect the increase in g?

According to the equation F = mg, the force of gravity is directly proportional to the mass of the object. This means that as the mass of lead increases, the force of gravity acting on it will also increase.

4. Can dimensional analysis be used to show the increase in g for other objects?

Yes, dimensional analysis can be applied to any object to show the increase in g due to an increase in mass. This is because the equation F = mg is a universal law that applies to all objects in a gravitational field.

5. Why is dimensional analysis an important tool for scientists?

Dimensional analysis allows scientists to convert between different units of measurement and ensure the accuracy of their calculations. It also helps to identify relationships between different physical quantities, such as mass and force, which can aid in understanding the underlying principles of nature.

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