# Help Evaluating Mathematical Modelling of Physical Problems

Thank you for setting my down that path, I will do some research and get back to you in a moment whether air resistance or friction is more significant.
I am just evaluating question 3 and then will reply to you with my thoughts...

Thank you very much for all of your help I really appreciate it • PeroK
Question 3)

This is a reasonable model as 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. Although, 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.

PeroK
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Question 3)

This is a reasonable model as 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. Although, 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.
Using this model, what would the tension be in the ropes? Is that realistic?

Would the tension be T=mg+ma? Or would it be that the tension is negligible?

PeroK
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Would the tension be T=mg+ma? Or would it be that the tension is negligible?
The question says constant speed. And nothing about going up hill.

The question does state that it is horizontal, maybe this means that it remains on a level surface also? Using F=ma would this mean that the tension is proportional to the acceleration, it is also constant? If acceleration is proportional to the force F as well as the tension increased acceleration would be contribute to increased force F, which causes proportional increase of tension T. Therefore, the higher acceleration - the higher the tension. When travelling downhill, objects will accelerate wheras when moving uphill they will decelerate and on a flat surface, assuming that there is little friction, they will then maintain a constant speed. So this model is not suitable in that it should not assume that accleration is constant if there is a change in altitude, as this would disrupt the proportional value of the tension?

PeroK
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That's an intetesting take. If I see constant speed in a question I assume acceleration is zero.

Where do these forces come from?

That's an intetesting take. If I see constant speed in a question I assume acceleration is zero.

Where do these forces cone from?
Sorry, I made a mistake, I mistook the acceleration as constant not the speed. I have puzzled myself.

That's an intetesting take. If I see constant speed in a question I assume acceleration is zero.

Where do these forces come from?
If the speed is constant then the acceleration would be zero. In accordance with F=ma, if a is zero, then F will zero and since the tension is proportional to the acceleration, would it is also be zero?

PeroK
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If the speed is constant then the acceleration would be zero. In accordance with F=ma, if a is zero, then F will zero and since the tension is proportional to the acceleration, would it is also be zero?
Yes.

So this would not be realistic, since there would be a least some tension in the ropes, it could not be zero?

PeroK
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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.

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.

PeroK
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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.

PeroK
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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.

PeroK
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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."

PeroK
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Go with that.

Should I not improve it somehow?

PeroK