## [Physics] Adding forces

**Moderators:** gmalivuk, Moderators General, Prelates

### [Physics] Adding forces

Now, I know there's a way of adding forces which, when Googled, shows you millions of results; the free-body diagram.

I don't want to add forces like that.

Say, I've got an object with a certain forces applied to it.

-- 5N --> [Box] -- 10N -->

With a free-body diagram, the resultant force would be:

[Box] -- 15N -->

That's fine and all but I the way I want to add forces is like this:

-- 5N --> [Box] -- 10N -->

Result:

[Box] -- 10N -->

Notice the difference. I "expect" this behaviour because adding 5N of force (not resultant force) to a box with a resultant force of 10N doesn't add anything, you're not contributing anything. Uhh, I can't really explain this (which is why I can't even look it up on Google).

This gets even messier with forces in arbitrary angles =/

sqrt(8)N

/

[Box] -- 10N -->

Let's say the sqrt(8)N force is in the direction (2, 2), hence the sqrt(8) magnitude.

With a free body diagram, the total force would be:

(12, 2)

However, with this, "other" way of adding forces, it shouldn't just add 2,2 to 10,0.

I've tried thinking of ways to get the result algorithmically but I don't even know what I expect the result to be.

Anyone know what I'm getting at? =/

I've thought about using the dot-products of the vectors and whatnot but I can't wrap my head around the results I really expect.

I just know that I don't want a free-body diagram because it treats all forces with equal weighting and uses them to find a resultant force.

What I want is, like:

+ If forces A and B are in the exact same direction, the larger magnitude will be taken

+ If forces A and B have directly opposite directions, then the result is (A + B)

+ If forces A and B don't fit in the above two conditions, then the result is ???;

if A, has a larger magnitude, then the resultant force should be mostly in the direction of A but a little in the direction of B

if B, has a larger magnitude, then the resultant force should be mostly in the direction of B but a little in the direction of A

The free-body diagram is, like:

+ If forces A and B are in the exact same direction, then the result is (A + B)

+ If forces A and B have directly opposite directions, then the result is (A + B)

+ If forces A and B don't fit in the above two conditions, then the result is (A + B)

I don't want to add forces like that.

Say, I've got an object with a certain forces applied to it.

-- 5N --> [Box] -- 10N -->

With a free-body diagram, the resultant force would be:

[Box] -- 15N -->

That's fine and all but I the way I want to add forces is like this:

-- 5N --> [Box] -- 10N -->

Result:

[Box] -- 10N -->

Notice the difference. I "expect" this behaviour because adding 5N of force (not resultant force) to a box with a resultant force of 10N doesn't add anything, you're not contributing anything. Uhh, I can't really explain this (which is why I can't even look it up on Google).

This gets even messier with forces in arbitrary angles =/

sqrt(8)N

/

[Box] -- 10N -->

Let's say the sqrt(8)N force is in the direction (2, 2), hence the sqrt(8) magnitude.

With a free body diagram, the total force would be:

(12, 2)

However, with this, "other" way of adding forces, it shouldn't just add 2,2 to 10,0.

I've tried thinking of ways to get the result algorithmically but I don't even know what I expect the result to be.

Anyone know what I'm getting at? =/

I've thought about using the dot-products of the vectors and whatnot but I can't wrap my head around the results I really expect.

I just know that I don't want a free-body diagram because it treats all forces with equal weighting and uses them to find a resultant force.

What I want is, like:

+ If forces A and B are in the exact same direction, the larger magnitude will be taken

+ If forces A and B have directly opposite directions, then the result is (A + B)

+ If forces A and B don't fit in the above two conditions, then the result is ???;

if A, has a larger magnitude, then the resultant force should be mostly in the direction of A but a little in the direction of B

if B, has a larger magnitude, then the resultant force should be mostly in the direction of B but a little in the direction of A

The free-body diagram is, like:

+ If forces A and B are in the exact same direction, then the result is (A + B)

+ If forces A and B have directly opposite directions, then the result is (A + B)

+ If forces A and B don't fit in the above two conditions, then the result is (A + B)

### Re: [Physics] Adding forces

Just for clarification, are you arguing that the ocmmonly taught method od drawing free body diagrams isn't representative of what would really happen, or that you understand how and why they are drawn the way they are, but are suggesting a different system of representing the same thing?

For example, if yo uare pushign a large crate, it isn't budging, so I come along and push on it with you, do you think only the stronger of us will actually be exerting a force on the crate?

For example, if yo uare pushign a large crate, it isn't budging, so I come along and push on it with you, do you think only the stronger of us will actually be exerting a force on the crate?

### Re: [Physics] Adding forces

are you arguing that the ocmmonly taught method od drawing free body diagrams isn't representative of what would really happen

No, I'm not arguing that. (I wouldn't dare to!)

or that you understand how and why they are drawn the way they are, but are suggesting a different system of representing the same thing

I'm not suggesting a different system for representing the same thing.

I'm trying to represent a different thing..

For example, if yo uare pushign a large crate, it isn't budging, so I come along and push on it with you, do you think only the stronger of us will actually be exerting a force on the crate?

Yeah, I think you've got what I'm driving at.

### Re: [Physics] Adding forces

What if someone strong is pushing one way, and two weaker people are pushing against each other, one with the strong one the other against him.

-> strong

<- weak

-> weak

We could say that the two weak cancel and thus we have only the strong left. Or we could say that the one weak doesn't matter since the strong is pushing the same way, thus we just subtract the other weak. Which would it be.

Oh and since we are not discussing the real world, but a fictional one where forces add differently, this should probably be moved to fictional science.

-> strong

<- weak

-> weak

We could say that the two weak cancel and thus we have only the strong left. Or we could say that the one weak doesn't matter since the strong is pushing the same way, thus we just subtract the other weak. Which would it be.

Oh and since we are not discussing the real world, but a fictional one where forces add differently, this should probably be moved to fictional science.

### Re: [Physics] Adding forces

What I want is, like:

+ If forces A and B are in the exact same direction, the larger magnitude will be taken

+ If forces A and B have directly opposite directions, then the result is (A + B)

I suspect that the reason you want the first feature is because of the everyday intuition that if someone strong is pulling a boulder and you're walking behind it then you don't actually have to push it to accelerate the rock and can just let the other guy pull it. If this is wrong please correct me.

Note that in that situation you're actually NOT applying a force at all though. Also note that if you DID push, then they wouldn't have to pull as hard. Moreover if they decided to pull as hard as they did before, the rock would accelerate more. If you feel like your push doesn't have an effect it's because you're not actually pushing. So it's simply not true that the smaller force has no effect, and your suggestion for adding forces in that way doesn't actually represent anything, which is why it's not used.

Our universe is most certainly unique... it's the only one that string theory doesn't describe.

### Re: [Physics] Adding forces

Notice the difference. I "expect" this behaviour because adding 5N of force (not resultant force) to a box with a resultant force of 10N doesn't add anything, you're not contributing anything. Uhh, I can't really explain this (which is why I can't even look it up on Google).

To expand on what Tchebu said, my guess is your intuition is telling you the following:

Suppose there is a boulder that, due to friction, won't move unless 10N is applied. You are thinking that if one person pushes it with 9N from behind, and one person pulls with 2N from in front, that the boulder won't move. But it really will. If the person in front doesn't do his bit, the boulder won't move, but if he does, it will.

The forces really do add up like a free-body diagram prescribes. That's why it's used after all. And that's why you can't find your model on Google, because it doesn't match our physical laws.

### Re: [Physics] Adding forces

elasto wrote:Notice the difference. I "expect" this behaviour because adding 5N of force (not resultant force) to a box with a resultant force of 10N doesn't add anything, you're not contributing anything. Uhh, I can't really explain this (which is why I can't even look it up on Google).

To expand on what Tchebu said, my guess is your intuition is telling you the following:

Suppose there is a boulder that, due to friction, won't move unless 10N is applied. You are thinking that if one person pushes it with 9N from behind, and one person pulls with 2N from in front, that the boulder won't move. But it really will. If the person in front doesn't do his bit, the boulder won't move, but if he does, it will.

The forces really do add up like a free-body diagram prescribes. That's why it's used after all. And that's why you can't find your model on Google, because it doesn't match our physical laws.

This is also how ouija boards 'work'. No individual pushes/pulls on the glass hard enough for it to move, but together it is enough. This is why all participants will validly claim that they didn't move it, but come to the invalid conclusion that it moved by itself.

### Re: [Physics] Adding forces

Ouija boards don't work.jaap wrote:This is also how ouija boards 'work'. No individual pushes/pulls on the glass hard enough for it to move, but together it is enough. This is why all participants will validly claim that they didn't move it, but come to the invalid conclusion that it moved by itself.

Last edited by screen317 on Wed May 22, 2013 6:02 pm UTC, edited 1 time in total.

- Xanthir
- My HERO!!!
**Posts:**5413**Joined:**Tue Feb 20, 2007 12:49 am UTC**Location:**The Googleplex-
**Contact:**

### Re: [Physics] Adding forces

Sigh, thus the scare quotes.

(defun fibs (n &optional (a 1) (b 1)) (take n (unfold '+ a b)))

- thoughtfully
**Posts:**2253**Joined:**Thu Nov 01, 2007 12:25 am UTC**Location:**Minneapolis, MN-
**Contact:**

### Re: [Physics] Adding forces

Could've fooled me, but they seem to have some significant psycological effects upon the participants.

### Re: [Physics] Adding forces

What exactly *do* you intend to represent with such a system?

Vector-summing forces to get a resultant force isn't a limited special case; it's how forces work. Not summing forces isn't even a coherent notion - if I push on something with both hands, is that one force or two? You can't even get around that by recognizing that both hands are part of the same larger object; you still have the same problem if I wear gloves. And does a pushing hand exert one single force, or should I count separately for the palm and each finger? What if 30% of the force is through the palm, but 14% through each finger - should I count only the palm's 30%, or the combined 70% from the fingers?

Really, the forces we put on a free-body diagram are *already* vector sums - they are the net result of countless interactions on atomic scales. But drawing septillions of arrows on a free-body diagram is tricky, so we abstract them into a single combined force. There's no reason to stop summing at some arbitrarily-chosen level of abstraction.

If there are 10N of force on the box, and you apply another 5N, you are indeed contributing something: namely, 5N of force. The box will now undergo 50% more acceleration.

If there are 10N of force on the box before *and* after you begin applying 5N, then something else was applying 5N and stopped when you started.

Your intuition may indeed expect otherwise, but that just means your intuition is inaccurate and needs to be adjusted.

Vector-summing forces to get a resultant force isn't a limited special case; it's how forces work. Not summing forces isn't even a coherent notion - if I push on something with both hands, is that one force or two? You can't even get around that by recognizing that both hands are part of the same larger object; you still have the same problem if I wear gloves. And does a pushing hand exert one single force, or should I count separately for the palm and each finger? What if 30% of the force is through the palm, but 14% through each finger - should I count only the palm's 30%, or the combined 70% from the fingers?

Really, the forces we put on a free-body diagram are *already* vector sums - they are the net result of countless interactions on atomic scales. But drawing septillions of arrows on a free-body diagram is tricky, so we abstract them into a single combined force. There's no reason to stop summing at some arbitrarily-chosen level of abstraction.

MrJustin wrote:I "expect" this behaviour because adding 5N of force (not resultant force) to a box with a resultant force of 10N doesn't add anything, you're not contributing anything. Uhh, I can't really explain this (which is why I can't even look it up on Google).

If there are 10N of force on the box, and you apply another 5N, you are indeed contributing something: namely, 5N of force. The box will now undergo 50% more acceleration.

If there are 10N of force on the box before *and* after you begin applying 5N, then something else was applying 5N and stopped when you started.

Your intuition may indeed expect otherwise, but that just means your intuition is inaccurate and needs to be adjusted.

No, even in theory, you cannot build a rocket more massive than the visible universe.

### Re: [Physics] Adding forces

Just to play Devil's Advocate, if you have two forces pushing on the box, one bigger than the other, then the greater magnitude force is going to accelerate the box away from whatever's providing the lesser force - eg you can't stand behind a car and push it forward if the engine has already pushed the car away from you.

Yes, I'm aware that "a force" (pure vector, no other info) has no mass and can therefore "keep up" whatever the acceleration, I'm just looking for a real life example to understand OP's confusion.

Yes, I'm aware that "a force" (pure vector, no other info) has no mass and can therefore "keep up" whatever the acceleration, I'm just looking for a real life example to understand OP's confusion.

### Re: [Physics] Adding forces

Well obviously. If you aren't pushing on the car, you wouldn't draw the arrow on the object in the free body diagram though. If the car is accelerating away from you and you can't keep up, how are you touching it? That's not rationale for the OP's strange "system."The Geoff wrote:Just to play Devil's Advocate, if you have two forces pushing on the box, one bigger than the other, then the greater magnitude force is going to accelerate the box away from whatever's providing the lesser force - eg you can't stand behind a car and push it forward if the engine has already pushed the car away from you.

Yes, I'm aware that "a force" (pure vector, no other info) has no mass and can therefore "keep up" whatever the acceleration, I'm just looking for a real life example to understand OP's confusion.

- Xanthir
- My HERO!!!
**Posts:**5413**Joined:**Tue Feb 20, 2007 12:49 am UTC**Location:**The Googleplex-
**Contact:**

### Re: [Physics] Adding forces

I actually suspect that *is* the OP's motivation, just not well stated. Eir intuition is likely exactly that the larger force will accelerate the box away from the smaller force, so you should only consider the larger one when doing math.

(defun fibs (n &optional (a 1) (b 1)) (take n (unfold '+ a b)))

### Re: [Physics] Adding forces

There is no smaller force then. We already don't include forces that aren't interacting with the object.Xanthir wrote:I actually suspect that *is* the OP's motivation, just not well stated. Eir intuition is likely exactly that the larger force will accelerate the box away from the smaller force, so you should only consider the larger one when doing math.

### Re: [Physics] Adding forces

screen317 wrote:There is no smaller force then. We already don't include forces that aren't interacting with the object.Xanthir wrote:I actually suspect that *is* the OP's motivation, just not well stated. Eir intuition is likely exactly that the larger force will accelerate the box away from the smaller force, so you should only consider the larger one when doing math.

The smaller force is acting, just with less magnitude.

- eternauta3k
**Posts:**519**Joined:**Thu May 10, 2007 12:19 am UTC**Location:**Buenos Aires, Argentina

### Re: [Physics] Adding forces

This isn't science.

### Re: [Physics] Adding forces

brenok wrote:screen317 wrote:There is no smaller force then. We already don't include forces that aren't interacting with the object.Xanthir wrote:I actually suspect that *is* the OP's motivation, just not well stated. Eir intuition is likely exactly that the larger force will accelerate the box away from the smaller force, so you should only consider the larger one when doing math.

The smaller force is acting, just with less magnitude.

If the smaller force is "somebody trying to push on the box, but the box outran them", then no it isn't.

But forces aren't objects that have positions - forces are exerted by objects that have positions. A person trying to push on a box, but unable to keep up with it, will exert no force; a rocket engine attached to the box will keep exerting force even if the box accelerates much faster than the rocket's thrust alone would allow.

And of course, that all has nothing to do with adding forces on the box, it's just a question of which forces are actually acting on the box in the first place.

No, even in theory, you cannot build a rocket more massive than the visible universe.

### Re: [Physics] Adding forces

Okay, lets go slowly, so that I don't get lost. Xanthir said:

Which means, the OP's intuition is that, even if two forces are already acting on a body, you should discard the smaller one (or, at least, is what I understood). I consider this intuition false.

Then screen said:

I disagreed. You can see on the OP that there are two forces interacting with the object on the initial example:

I hope that clears any confusion.

Which means, the OP's intuition is that, even if two forces are already acting on a body, you should discard the smaller one (or, at least, is what I understood). I consider this intuition false.

Then screen said:

screen317 wrote:There is no smaller force then. We already don't include forces that aren't interacting with the object.

I disagreed. You can see on the OP that there are two forces interacting with the object on the initial example:

MrJustin wrote:Say, I've got an object with a certain forces applied to it.

-- 5N --> [Box] -- 10N -->

Result:

[Box] -- 10N -->

I hope that clears any confusion.

### Re: [Physics] Adding forces

I kinda hope the OP will come back and be all "Yes yes, I understand how physics actually works, I just want to implement this in code for some project to demonstrate why adding forces in this wrong method is wrong" or some such. They do know that dot products are a thing, which at least in my schooling came well after how forces add was taught, so perhaps it's for some weird coding implementation of crazy different physics world or something. (I'm not sure I believe this, but maybe...)

I suppose they'd probably just want to break up forces on an angle to deal with one component at a time, so under some circumstances you'd have only the component in the x direction actually contributing anything, with the y component being lost to their desire take the the max of all forces in a given direction, and then add the final two surviving perpendicular components as normal. It's still weird though, and of course it should be emphasized that it doesn't represent how things actually work in real life.

edit: It occurs to me that this may result in forces that vary depending on your choice of coordinate system. This is of course a problem if you want to represent anything even remotely realistic.

I suppose they'd probably just want to break up forces on an angle to deal with one component at a time, so under some circumstances you'd have only the component in the x direction actually contributing anything, with the y component being lost to their desire take the the max of all forces in a given direction, and then add the final two surviving perpendicular components as normal. It's still weird though, and of course it should be emphasized that it doesn't represent how things actually work in real life.

edit: It occurs to me that this may result in forces that vary depending on your choice of coordinate system. This is of course a problem if you want to represent anything even remotely realistic.

Last edited by Dopefish on Mon May 27, 2013 1:22 am UTC, edited 1 time in total.

### Re: [Physics] Adding forces

brenok wrote:Okay, lets go slowly, so that I don't get lost. <snip for brevity>

Perhaps I've misunderstood what you meant this to be a reply to:

brenok wrote:The smaller force is acting, just with less magnitude.

If that's a reply to the notion that the smaller force isn't acting at all, yes, I agree (eg, it exerts 5N, not 0N). In my previous response, I had been interpreting it as a response to the notion that the object was being accelerated away from the smaller force - that if the object is accelerated away from the smaller force, it will continue acting (eg, 3N instead of 5N). My apologies for the confusion.

No, even in theory, you cannot build a rocket more massive than the visible universe.

### Re: [Physics] Adding forces

No need to apologise, just glad we agree. And @Dopefish, I didn't think about that. Lets hope, too.

### Re: [Physics] Adding forces

Then the OP clarifies:brenok wrote:I disagreed. You can see on the OP that there are two forces interacting with the object on the initial example:MrJustin wrote:Say, I've got an object with a certain forces applied to it.

-- 5N --> [Box] -- 10N -->

Result:

[Box] -- 10N -->

I hope that clears any confusion.

He wants to add 5N of force. That's the problem. He thinks adding 5N of force doesn't do anything.Notice the difference. I "expect" this behaviour because adding 5N of force (not resultant force) to a box with a resultant force of 10N doesn't add anything, you're not contributing anything. Uhh, I can't really explain this (which is why I can't even look it up on Google).

### Who is online

Users browsing this forum: No registered users and 6 guests