Simplification assumptions in physics problems

[Amad27]

Hello,

Recently, I had been looking at Physics problems, and Physics word problems to be more specific.

My question is, are simplifying assumptions required in physics-math-related problems?

Like, you must neglect air resistance because it is a simplifying assumption right? Is this true?

And the answer with the simplest model will be correct because it is a convention to make simplifying assumptions in physics problems when writing, reading and answering them right?? I just want to confirm this thought.

From http://nrich.maths.org/6631

Thanks!

 

[SteamKing]

Simplifying assumptions are not required, but in the absence of information, they sometimes must be made in order to arrive at a solution, recognizing the solution obtained thus may necessarily be only approximate.

For example, you could work out all of your free-fall problems taking into account air resistance, but if the distance an object falls is very small, the amount of time it takes an object to strike the ground neglecting air resistance will only be slightly shorter than the time calculated taking air resistance into account, at the greater cost in equation complexity and the amount of time you spend obtaining a solution.

 

[Amad27]

Hello @SteamKing,

So suppose, I have a problem from a Physics Textbook,

"A bowling ball with constant speed hits the pins at the end of the bowling lane at 16.5m long. The bowler hears the sound of the ball hitting the pins at 2.50s after the ball is released from his hands. What is the speed of the ball? The speed of sound is 340 m/s" (Giancoli Physics 6e P39).

Some data here is not given such as friction or some sort of resistance, slowing down the ball. This is sort of ambiguous.

So here, you make a simplifying assumptions that there is no friction and also that there is no resistance of some sort.

Then why is this just an approximation as you state above "recognizing the solution obtained thus may necessarily be only approximate."

 

[Nugatory]

Then why is this just an approximation as you state above "recognizing the solution obtained thus may necessarily be only approximate."

The question is asking "What is the speed of the ball?". That question has an exact answer - in principle we can measure the speed of the ball to whatever degree of accuracy we want.

When we do the calculation with various simplifying assumptions, we aren't going to come up with that exact precise value. Friction is a non-issue in this problem (we've been told the ball moves at a constant speed), but there are other ambiguities - for example, the sound is spread out over time - that keep our calculation from being spot-on to the 98th decimal place.

And if our calculation isn't giving the exact same result as a measurement, then it's pretty much by definition an approximation.

 

[Amad27]

Hello @Nugatory,

My point is --

You must make simplifying assumptions.

The first comment stated the answer may only be an approximate if you use simplifying assumptions.

Then every answer is an approximate.

For example, when the ball rolls down the lane, you must make an assumptions that it doesn't roll off to the side. Which is another simplifying assumption now, isn't it?

Thanks!

 

[sophiecentaur]

Hello,

Recently, I had been looking at Physics problems, and Physics word problems to be more specific.

My question is, are simplifying assumptions required in physics-math-related problems?

Like, you must neglect air resistance because it is a simplifying assumption right? Is this true?

And the answer with the simplest model will be correct because it is a convention to make simplifying assumptions in physics problems when writing, reading and answering them right?? I just want to confirm this thought.

From http://nrich.maths.org/6631

Thanks!

When you are presented with a 'Physics Problem', and the problem is from a reputable source, you can assume that what you may think is 'missing data' has been deliberately left out. That was someone else's decision and the problem was stated in a way that you have a chance of answering it (an ideal model).
In Real Life, when you are investigating some phenomenon, you also start off by assuming the simplest conditions and then, using experience, you decide what other factors are relevant. But you can really get it wrong, if you leave out a factor. That will reveal itself when you try to tie your experimental results with your model. Time to look again and see what you should have included.

 

[voko]

While I agree completely with sophiecentaur, I would like to restate that a bit. Physics is always about making a model. School-level physics, or cutting edge research physics, it is all the same. We make a model, and that always implies making simplifying assumptions. The reality is infinitely more complex than any model we can make, so any model is about simplifying it. Sometimes, we may not even understand that we make simplifying assumptions! For example, till about one hundred years ago, no one really understood that the notions of "absolute time" and "absolute simultaneity" were simplifying assumptions, it took Mr Einstein to explain that to us.

 

[Vanadium 50]

A bowling ball with constant speed

Some data here is not given such as friction or some sort of resistance, slowing down the ball.

But the information is given. The ball does not slow down. That's what constant speed implies.

 

[Amad27]

Hello,

@Vanadium 50 my point is that the simplifying is required.

Does the problem tell you that the ball makes it all the way to the end of the lane? You still assume it does for simplicity.

 

[A.T.]

Does the problem tell you that the ball makes it all the way to the end of the lane?

Yes.

 

[Amad27]

Hello,

So really, what is the final verdict? Do you make simplification assumptions as a convention when doing text-problems in Physics?

Thanks!

 

[HallsofIvy]

What has already been said: If there are critical parameters you have not been given, then, in order to do the problem you will have to make assumptions as to their value. When you do that, if you are not given other information about their value, there would be no reason not to make take the simplest values. Of course, you should state those assumptions in your solution.

If you do not do that, the only thing you could do with any physics problem is throw up your hands and declare that there is not accurate enough information to solve the problem. That would make physics a pretty meaningless science!

 

[Amad27]

@HallsofIvy , Right, Take a look at a better example,

"A helicopter is ascending vertically with a speed of 5.2 m/s. At a height of 125 m above the earth, a package is dropped from a window. How much time does it take for the package to reach the ground?" (Giancoli Physics 48-49).

This Physics problems has some simplification assumptions needed. One of them is that,

(1) The helicopter drops the package at exactly 125m.
(2) The package does not explode in air
(3) The package does not break when it reaches the ground
(4) The helicopter doesn't run out of fuel when going to 125m vertically.
(5) Must NEGLECT air resistance.
(n) assumption
(n+1) another assumption.

The list can go on infinitely, which is why these simplification assumptions are often if not always left unstated in the problem.

It is more of a convention/ fundamental property of these types of problems =)

Do you think what I have written (here) is of good knowledge??

Thanks!

 

[Vanadium 50]

Do you think what I have written (here) is of good knowledge??

No. There is no insight here other than "if the problem were different, the answer would be too.

 

[voko]

(1) The helicopter drops the package at exactly 125m.

No. First, 125 m is given; second, there is no requirement for that to be 125 m exactly, and 125 m specifies the precision.

(2) The package does not explode in air

No. The problem asks when the package reaches the ground, so its integrity until that moment is part of the problem.

(3) The package does not break when it reaches the ground

No. You are not supposed to care what happens when it reaches the ground.

(4) The helicopter doesn't run out of fuel when going to 125m vertically.

No. You are not supposed to care whether the helicopter runs out of fuel.

(5) Must NEGLECT air resistance.

Possibly. This is the first instance in your long list when you should really think about making an assumption.

 

[Amad27]

@voko I will show you an important physics example from a calculus-based physics book.

A trough is 12 feet long and 3 feet across. Its ends are isosceles triangles with altitudes of 3 feet.

1. Water is being pumped into the trough at 2 cubic feet per minute. How fast is the water level rising when the depth is 1 feet?
   

This is one of my favorite examples. If you look at it, a very important simplifying assumption is that

(1) Water is not LEAKING through the trough, so there is no leakage.

This is a critical assumptions because

[itex] dV/dt = du/dt - dk/dt[/itex] where [itex]du/dt[/itex] is the rate at which water enters, and [itex]dk/dt[/itex] is the rate at which water leaks or leaves.

So, does this example sort of show that you must make simplifying assumptions? And they need not be stated because simplifying assumptions are conventions of these problems. As shown in http://nrich.maths.org/6631

Ideas? Thanks a lot!

 

[voko]

I stated earlier that one always makes assumptions when doing physics. There is no need to repeat that ad nauseam.

Your latest example shows nothing but nitpicking. A trough means a vessel capable of holding liquids. A normal trough does not leak, and there is no need to mention that specifically.

 

[Amad27]

I stated earlier that one always makes assumptions when doing physics

Thanks @voko ,

So, to finish off the topic, do you agree with the statement (in one piece):

You make simplifying assumptions in physics because it is more-or-less a convention of these types of problems.

I thought of this "convention," because when you said "I stated earlier that one always makes assumptions when doing physics"

 

[voko]

You make simplifying assumptions in physics because it is more-or-less a convention of these types of problems.

No, I do not agree with this one piece. The reasons why assumptions are made were stated earlier by me and others, and it is about time you tried to understand that, rather than promoting your misconceptions.

 

[Nugatory]

So, to finish off the topic, do you agree with the statement (in one piece):

You make simplifying assumptions in physics because it is more-or-less a convention of these types of problems.

No, that is not the right way of thinking about it. You are confusing "physics" with "physics problems in physics textbooks"; the latter is learning physics, not doing physics.

Yes, there are all sorts of assumptions buried in the problems you'll find in a physics textbook. For example, so many elementary textbook problems ignore air resistance without saying so that you might reasonably conclude that's it's "convention" that air resistance should be ignored unless you're told otherwise. But these are just practice problems, designed to teach you about the relationship between various fundamental concepts and to give you practice with the tools in your mathematical toolbox.

Suppose you are confronted with a real problem: Here is a physical system; here's what we know about it; how do we expect it to behave? The first thing you'll have to do is decide which effects are important enough to model and which will be small enough to ignore... and you'll be on your own, no "convention" to guide you. In many, even most cases, it will depend on the accuracy of the result that you need. If you're testing the proposition that gravitational mass is equal to inertial mass, you can ignore air resistance if you're dropping iron and brass balls and lucky to get measurements that are accurate to one part in hundred; Eotvos experiments, not so much.

 

[Amad27]

Yes, there are all sorts of assumptions buried in the problems you'll find in a physics textbook. For example, so many elementary textbook problems ignore air resistance without saying so that you might reasonably conclude that's it's "convention" that air resistance should be ignored unless you're told otherwise. But these are just practice problems, designed to teach you about the relationship between various fundamental concepts and to give you practice with the tools in your mathematical toolbox.

Hello,

My main focus is textbook-physics problems.

Then how do you suggest making assumptions? Which assumptions should you make?

Thanks to @Nugatory and @voko and everybody helping me =) I really appreciate it!

 

[Nugatory]

Then how do you suggest making assumptions? Which assumptions should you make?

For textbook problems?
Practice, ideally with the guidance of someone more experienced than you, but you can do it on your own if need be. When you get an answer matches the solution in the textbook's answer key then you've done it right. If you can't get an answer, then you're doing something wrong. But there really truly is no substitute for practice - you aren't following recipes from a cookbook, you're filling your mental toolbox with tools and acquiring the skill needed to use them effectively.

 

[Amad27]

For textbook problems?
Practice, ideally with the guidance of someone more experienced than you, but you can do it on your own if need be. When you get an answer matches the solution in the textbook's answer key then you've done it right. If you can't get an answer, then you're doing something wrong. But there really truly is no substitute for practice - you aren't following recipes from a cookbook, you're filling your mental toolbox with tools and acquiring the skill needed to use them effectively.

Hello @Nugatory , thanks for replying =)

But the question is, when answering, which assumptions should I make??

Let me ask something, tell me if the following are assumptions or not assumptions

(1) The water-trough (from example) has a leak.
(2) The water-trough (from example) has NO leak.

Is (2) an assumption? Because generally when people talk about assumptions they mean the existence, not the absence.

For me, it **SEEMS** like (1) is an assumption and (2) is a neglecting. [just opinion, doesn't have to be true].

Thanks! A lot =D

 

[Nugatory]

Because generally when people talk about assumptions they mean the existence, not the absence.

In English, that distinction does not exist. You'll hear people saying "We assume this effect is insignificant" all the time.

 

[Amad27]

In English, that distinction does not exist. You'll hear people saying "We assume this effect is insignificant" all the time.

Hi @Nugatory thanks for replying =D

Ok, so what assumptions should we make when doing textbook-physics problems??

Because when I generally see "assumption," it is related with existence. So I was wondering if we make any assumptions at all? Like we just don't make assumptions, meaning we neglect leaks etc..

Help please?

Thanks @Nugatory, I'm very grateful for your help =D

 

[Amad27]

In English, that distinction does not exist. You'll hear people saying "We assume this effect is insignificant" all the time.

Actually @Nugatory scratch that. One person here said,

When you are presented with a 'Physics Problem', and the problem is from a reputable source, you can assume that what you may think is 'missing data' has been deliberately left out.

This could mean that a convention of these problems (textbook) is that they provide all information before-hand. What do you say?

Thanks a lot!

 

[sophiecentaur]

Actually @Nugatory scratch that. One person here said,
This could mean that a convention of these problems (textbook) is that they provide all information before-hand. What do you say?

Thanks a lot!

Yes; absolutely. You have to answer the question and not introduce any of your own ideas about improving the 'experiment' described.
If it were ann arithmetic question, you wouldn't start to consider the possible changing prices of apples when you have been given the price in the problem. The problem could have been set fifty years ago and you could possibly think that inflation should be introduced.
When the time is appropriate to introduce complications then the questions you will be given will get harder.
This should not disappoint you. There's nothing to stop you from going ahead of your lessons (if you really can cope and with the help of a textbook) and seeing how other factors affect things. Exam questions (relevant to most Physics courses) are marked using a Mark Scheme and the numerical right answer is needed for full marks. Examiners don't have time (a few seconds to mark some questions) to analyse your approach and give you marks for thinking outside the box. They want (and you need) the boring conventional answer and you should go along with that until you emerge into 'research levels' of study.

 

[A.T.]

these problems (textbook) is that they provide all information before-hand.

Sounds like a good idea for a textbook, which cannot be asked for additional info.

 

[sophiecentaur]

There are no prizes for rewriting an exam or textbook question.

 

[Amad27]

There are no prizes for rewriting an exam or textbook question.

Thanks @sophiecentaur , so one last question on this,

So textbook problems provide all information before-hand? This is convention/definition right?? Thanks! (This was one last concept question =D)

 

[sophiecentaur]

Thanks @sophiecentaur , so one last question on this,

So textbook problems provide all information before-hand? This is convention/definition right?? Thanks! (This was one last concept question =D)

I couldn't speak for all textbooks and some questions can be mis-printed, badly written or just plain bad ones. I can't imagine why you keep asking what is effectively the same question. Are you hoping for a different answer? You have to ask yourself - what would be the point of a totally open question, where data is missing?

 

[Amad27]

I couldn't speak for all textbooks and some questions can be mis-printed, badly written or just plain bad ones. I can't imagine why you keep asking what is effectively the same question. Are you hoping for a different answer? You have to ask yourself - what would be the point of a totally open question, where data is missing?

Hello @sophiecentaur,

My dilemma is that somehow I get winded up into philosophy.

Can I ask you something? Is this question a philosophical question?

The problem is philosophical questions never really have proper answers.

If this is philosophy, would you suggest accepting this fact and moving on??

Thanks! A lot

 

[sophiecentaur]

Hardly philosophical - just pragmatic. How does someone know they have the right answer if the question has not been defined? Where the framework is well defined (as in elementary Physics) and you want to learn how to use it, open ended questions are just counterproductive.
Move on - as you suggest. There is nothing philosophical about the dynamics of a bowling ball.

 

[Amad27]

Hardly philosophical - just pragmatic. How does someone know they have the right answer if the question has not been defined? Where the framework is well defined (as in elementary Physics) and you want to learn how to use it, open ended questions are just counterproductive.
Move on - as you suggest. There is nothing philosophical about the dynamics of a bowling ball.

Hello @sophiecentaur , I meant something a little different.

Is the question of why and how we make certain assumptions a philosophical question? Is it philosophy asking why we believe word problems require certain assumptions such as there is no leakage in the trough?

Because this sort of deals with existence and communication so I just thought it was philosophy.

**************And philosophy does not have an absolute answer, so the best way to go about it is to accept that word problems provide all information, without a reason of WHY. **************

What do you say?

 

[sophiecentaur]

Hello @sophiecentaur
**************And philosophy does not have an absolute answer,

What do you say?

And neither does Science. But most of Science starts from an entirely different place.
This thread should no longer be on this forum, imo. It should, rather, be somewhere in the 'lounge' as it is not helpful for someone who just wants to know Physics better.