Desperately Seeking Modelling Help: Expert Assistance for Homework Questions

  • Thread starter magicuniverse
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In summary, the first problem is to find a function that replaces the terms in the Q equation with expressions that are functions of T. The second problem asks for the relationship between position, x, and velocity. The solution is found by taking the derivative and using F=ma. The third problem asks for the relationship between position, x, and potential. The solution is found by taking the derivative and using F=m*(-dV/dx). The fourth problem asks for the relationship between position, x, and velocity over an interval. The solution is found by plotting the graph and taking the derivative.
  • #1
magicuniverse
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Homework Statement



I need some help with all of the questions in the attatchment but would love it if you could provide some help with the first question please.

Homework Equations



In the file.


The Attempt at a Solution



Dont be silly, I don't have a clue. If I could do it I wouldn't be posting here!
 

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  • #2
I don't like your tone: "Dont be silly"
 
  • #3
Well I was talking to the computer and trying to be lighthearted. Sorry if I really offended you.
 
  • #4
I would also point out that there is an enormous gap between "I don't have a clue" and "If I could do it". What you have posted appears to be a test (perhaps a practice test) for a class in mathematical modelling. Surely, you have had some instruction in this?

Problem 1 appears to be a matter of replacing some terms in the formula for Q by their expression as a function of T, the temperature. That is, the formula for Q involves viscosity [itex]\eta[/itex]; [itex]\eta[/itex] itself is a function of [itex]\overline{\nu}[/itex] which, in turn "is proportional to the square root of temperature". Q also is proportional to the radius, R, to the fourth power and (1/R) (dr/dT) is a constant.

For problem 2, you are given how the Velocity depends upon position, x, V(x).
Use F= ma. a= dV/dt= (dV/dx)(dx/dt)= V dV/dx.
 
  • #5
HallsofIvy said:
For problem 2, you are given how the Velocity depends upon position, x, V(x).
Use F= ma. a= dV/dt= (dV/dx)(dx/dt)= V dV/dx.

V(x) represents the potential here, not velocity.

magicuniverse said:
I don't have a clue.

We don't like that here. If you show a bit of effort, a lot of help will be readily forthcoming. I'll give you some hints anyway.

F = m*(-dV/dx). At equilibrium, F=0, so you can find the value of x.

For plotting the graph, take the derivative and see how it changes signs. Consider how V(x) behaves for fractional values and for x>1. Remember, it’s an even function.

For prob 1, you must have understood by now that what you have to find is dQ/Q in terms of dT.
 

FAQ: Desperately Seeking Modelling Help: Expert Assistance for Homework Questions

What is modelling?

Modelling is the process of creating a simplified representation of a system, phenomenon, or concept in order to understand, analyze, or predict its behavior.

Why is modelling important?

Modelling allows scientists to study complex systems, make predictions, and test hypotheses without the need for costly or time-consuming experiments. It also helps to identify gaps in our understanding and guide future research.

What are the steps involved in modelling?

The steps involved in modelling typically include defining the problem, collecting data, choosing an appropriate model, calibrating and validating the model, and using the model to make predictions or draw conclusions.

What are some common types of models?

Some common types of models include mathematical models, statistical models, physical models, and computer simulations. Each type of model has its own strengths and limitations, and the choice of model depends on the specific research question and available data.

What are some common challenges in modelling?

Some common challenges in modelling include selecting an appropriate model, obtaining accurate and reliable data, dealing with uncertainty and variability, and interpreting the results. It is important for scientists to be aware of these challenges and to carefully consider them when designing and interpreting their models.

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