# Help Evaluating Mathematical Modelling of Physical Problems

• lpettigrew
In summary, the conversation discusses three different mathematical models for various physical situations. The first model is for a ball being thrown vertically upwards, where it is modeled as a particle moving under constant gravity with no air resistance. The second model is for a puck being hit towards a goal in ice hockey, where the puck is modeled as a particle moving on a smooth surface. The third model is for a cart being pulled by two horses, where all objects are assumed to be particles and there is no resistance in the moving parts of the cart. The conversation also touches on the concept of an inextensible string and the importance of identifying weak points in a model to suggest improvements.
So this would not be realistic, since there would be a least some tension in the ropes, it could not be zero?

lpettigrew said:
So this would not be realistic, since there would be a least some tension in the ropes, it could not be zero?
Yes. Although "realistic" might be subtly different from good. Personally, I think c) is a poor question, since it's not clear what is the point of this model. What is the relevance of a small amount of tension in the ropes? As opposed to zero tension. What does it matter?

A better question would be a car at constant speed with no resisting forces. Then, the model would be bad because it would predict zero fuel consumption. That model would be practically useless.

PeroK said:
Yes. Although "realistic" might be subtly different from good. Personally, I think c) is a poor question, since it's not clear what is the point of this model. What is the relevance of a small amount of tension in the ropes? As opposed to zero tension. What does it matter?

A better question would be a car at constant speed with no resisting forces. Then, the model would be bad because it would predict zero fuel consumption. That model would be practically useless.

If the tension in the rope is proportional to the acceleration (which is zero), would this be like assuming the rope is tense and completely stationary since the force pulling the the rope by the horses must be balanced by an equal force pulling from the cart? The force of tension would act on an object opposing its movement and reducing its speed. Therefore, the significance of there being some tension, even a small amount, as opposed to zero tension is that it reduces the speed with which the horse and cart travel?

So I could state that this model is poor since finding the tension in the ropes has little effect on the motion of the cart. The model could be refined to take into account that the string may extend. Additionally, it may be preferable to account for the friction and other forces acting due to the moving parts of the cart at a later stage. Moreover, the string may be considered light (meaning that since its mass is very small compared to the other masses in question we can take it to be zero) since weight if the horses and cart far exceeds that of the string. It would also be worthy to take into account the mass of the horses and cart.
Although the extension of the rope is likely to be small so the assumption that the string is inextensible is fitting. Moreover, the statement that there is no resistance in the moving parts of the cart is reasonable if the cart is in optimal working order and is adequately maintained. It may be better to neglect the tension in the ropes since when the cart moves with constant speed the acceleration is equal to zero. According to F=ma, the force of the tension will be proportion to the acceleration, here being zero, so it is futile finding the tension if it has no effect.

Maybe you could say that more simply!

So I could state that this model is poor since it is states that the speed with which the cart travels is constant, menaing the acceleration is zero. Since the acceleration is proportional to the tension, this would mean that the tension in the rope is also equal to zero. therefore, it would be pointless to mathematically prove this.
Finding the tension in the ropes has little effect on the motion of the cart, since it is equal to zero, therefore, it may be better to neglect the tension in the ropes.

The model could be refined to take into account that the string may extend. Additionally, it may be preferable to account for the friction and other forces acting due to the moving parts of the cart at a later stage.

Maybe that's a bit better. I would look at improving your writing when you have time. You should try to write in shorter sentences that focus on one point at a time.

Merlin3189
Could you give an example of how I could do so? Admittedly I am trying to work on this but feel that I tend to include to much information than required, or just include unnecessary additional statements.

lpettigrew said:
Could you give an example of how I could do so? Admittedly I am trying to work on this but feel that I tend to include to much information than required, or just include unnecessary additional statements.
Could you give an example? I am working on this but tend to include too much information.

For example condensing my answer to question3 to be more concise.

"This model is poor since it is states that the speed with which the cart travels is constant, menaing the acceleration is zero. Since the acceleration is proportional to the tension, this would mean that the tension in the rope is also equal to zero. therefore, it would be pointless to mathematically prove this.
Finding the tension in the ropes has little effect on the motion of the cart, since it is equal to zero, therefore, it may be better to neglect the tension in the ropes.

The model could be refined to take into account that the string may extend. Additionally, it may be preferable to account for the friction and other forces acting due to the moving parts of the cart at a later stage."

Go with that.

Should I not improve it somehow?

That's up to you.

I am not sure how but I want to, I do not feel that it suitably and fully answers the question

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