Using dimensional analysis to create dimensionless equation

In summary, the conversation discusses the task of solving and creating a dimensionless equation from a given differential equation. The problem involves performing dimensional analysis and adjusting the equation by multiplying both sides with the gravitational constant G. The question at the end asks for clarification on the problem and its solution.
  • #1
astrofunk21
29
0

Homework Statement


I am tasked with solving and creating a dimensionless equation from a differential equation given.

Homework Equations


This is the given equation:

render.png

The Attempt at a Solution


When doing the dimensional analysis I see that we are left with units of [m-3][kg1][s-2].

These units are actually the units of the inverse of the gravitational constant G. So to make this equation dimensionless would I just multiple both sides by G? So we get this dimensionless equation (but not really since the left side isn't exactly dimensionless):

render.png


Would appreciate help on where to go with this! Thanks in advance
 
Physics news on Phys.org
  • #2
Please give the problem exactly as stated.
 
  • #3
Orodruin said:
Please give the problem exactly as stated.
Question: Solve and make a dimensional analysis in order to ensure the equation is really dimensionless.
 
  • #4
That is not the entire problem. It sounds like the very end of the problem text.
 
  • #5
What is c in the equation?
 

1. How does dimensional analysis help in creating dimensionless equations?

Dimensional analysis is a mathematical technique used to analyze the relationship between different physical quantities. By using this method, we can identify the relevant dimensions and units involved in a given equation and create a dimensionless form by canceling out these dimensions. This allows us to simplify the equation and make it more generalized and applicable to different situations.

2. What are the benefits of using dimensionless equations?

Dimensionless equations are beneficial because they are independent of any specific system of units. This means that they can be applied universally and are not limited to a particular measurement system. Additionally, dimensionless equations are more compact and easier to manipulate, making them useful in a variety of scientific and engineering fields.

3. Can any equation be made dimensionless using dimensional analysis?

No, not all equations can be made dimensionless through dimensional analysis. The equation must have a physical meaning and involve measurable quantities. Additionally, the equation should have a consistent set of units to be able to cancel out dimensions. If these criteria are met, then dimensional analysis can be applied to create a dimensionless form of the equation.

4. How does reducing dimensions in an equation affect its accuracy?

Reducing dimensions in an equation does not affect its accuracy as long as the equation is dimensionally correct. The dimensions and units are simply used to represent the physical quantities involved in the equation, and canceling them out does not change the actual relationship between these quantities. However, it is important to ensure that the equation is dimensionally consistent before applying dimensional analysis.

5. Can dimensional analysis be used in all areas of science?

Yes, dimensional analysis can be applied in various fields of science, including physics, chemistry, biology, and engineering. It is a fundamental tool in understanding the relationships between different physical quantities and can be used to solve problems and develop theories in a wide range of scientific disciplines.

Similar threads

Dimensional analysis on an Ising model solution
    • Advanced Physics Homework Help
Replies
9
Views
2K
Dimensional Analysis: Forster Energy Transfer equation
    • Introductory Physics Homework Help
Replies
2
Views
777
Temperature difference by Dimensional analysis.
    • Advanced Physics Homework Help
Replies
2
Views
877
Dimensional analysis - atomic bomb explosion radius
    • Advanced Physics Homework Help
Replies
7
Views
2K
Dimensional analysis of an equation of motion
    • Advanced Physics Homework Help
Replies
6
Views
2K
Dimensional Analysis - Schrödinger equation
    • Advanced Physics Homework Help
Replies
2
Views
3K
I Is "nondimensionalization" a misnomer?
    • Other Physics Topics
Replies
19
Views
1K
A What is Dimensional Transmutation?
    • High Energy, Nuclear, Particle Physics
Replies
1
Views
991
I am revisiting the mathematical formulation of quantum mechanics with the dimensional (MLT) perspective
    • Quantum Physics
Replies
14
Views
954
I How to ensure an equation is dimensionless when it includes "Debye"
    • Classical Physics
Replies
2
Views
634

Hot Threads

Recent Insights

Back
Top