# Simplification assumptions in physics problems

1. Sep 21, 2014

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!

2. Sep 21, 2014

### SteamKing

Staff Emeritus
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.

3. Sep 21, 2014

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."

4. Sep 21, 2014

### Staff: Mentor

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.

5. Sep 21, 2014

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 doesnt roll off to the side. Which is another simplifying assumption now, isnt it?

Thanks!

6. Sep 21, 2014

### sophiecentaur

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.

7. Sep 21, 2014

### 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.

8. Sep 21, 2014

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

9. Sep 21, 2014

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.

10. Sep 21, 2014

### A.T.

Yes.

11. Sep 21, 2014

Hello,

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

Thanks!

12. Sep 21, 2014

### HallsofIvy

Staff Emeritus
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!

13. Sep 21, 2014

@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 doesnt 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!

14. Sep 21, 2014

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

15. Sep 21, 2014

### voko

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

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

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

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

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

16. Sep 21, 2014

@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

$dV/dt = du/dt - dk/dt$ where $du/dt$ is the rate at which water enters, and $dk/dt$ 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!

17. Sep 21, 2014

### 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.

18. Sep 21, 2014

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"

19. Sep 21, 2014

### voko

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.

20. Sep 21, 2014

### Staff: Mentor

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.