Questions about momentum and force as well as normal force/friction

[cardboard_box]

TL;DR Summary

TL;DR: need helping clearing up some things about how momentum can "cause" a force as well as how the normal force and friction may relate to it (with examples)

DISCLAIMERS: if at any point in the text I state something wrong please do mention and correct how it will effect the rest of the arguments.

examples 1 and 2 are mainly to build up to the more important example 3 while allowing you to see if I made any wrong statements about the interactions before that.

with each of those examples the main point is *why* does a variable do what it does and *how* is it proportional.

while I know that friction and the normal force aren't dependent on surface area, I don't fully get it, wouldn't more surface area = more electrons pushing back = more friction/normal force?



example 1:
Lets say that I got 2 cubes which we will call cube 1 and cube 2, floating in a vacuum, I know the mass of both cubes as well as the velocity (and assume the velocity of cube 2 is 0 for simplicity) and whatever other parameters you may need to know (do mention them in answers). when cube 1 collides with the stationary cube 2 there is an impulse which causes changes in each of their momentum, We know that this is likely due to the normal force, which is also what prevents cube 1 from simply phasing into cube 2 and not changing any momentum. since this is a vacuum if I do not change any of the variables and repeat these actions as many times as I want the results shouldn't change, from this we can infer there must be a way to calculate the final momentum of each cube based on the information we know alone (no looking at the impulse itself). I understand that this is just the coefficient of restitution, but how exactly could we calculate it? what information would we need and how would each of them effect the outcome?


example 2:
assuming you've read and understood the example before I'd like to ask the same question but a bit different, if the 2 cubes instead of smashing into one another and not phasing in each other due to the normal force, instead barely touched each other's side in tangential matter, there should be a force of friction but since the normal force is 0 would that mean they would simply not interact at all? if so assume we do put an equal force against each of them so that they do have friction between them, if that friction is static then the cubes should act just as they did in the first example, but if its kinetic it should slow down the objects during contact, but it shouldn't be able to inverse the momentum of cube 1. according to this interaction the momentum of the 2 objects shouldn't matter at all in this question, since friction isn't dependent on mass or velocity, but why? it makes sense that an object with more inertia moving faster should have a different effect of friction.




example 3:
now lets think about how we can do this tangentially, assume this time that I got a spinning wheel that will touches a projectile (could be any but I'll refer to a ball) also imagine we got a nice hood as in the picture bellow so that the ball can't just leave the moment a force is applied

also assume the wheel doesn't have to touch the projectile tangentially like in the diagram (but if you treat it one way or the other please do elaborate on why you chose the amount of compression you chose) and that the hood has some friction so that the ball also rolls against it due to the wheel pushing it (again if you have any insight on what hood friction differences do tell).

how would the surface collision like in example 2 work on a wheel (which has infinite sides) work? if I gave you a known projectile which you know everything about and told you to shoot it for me at x velocity, how would you change the wheel variables and why?



if anyone spots information I missed please tell, and thank you.

 

[anuttarasammyak]

You pose some questions. What are your own conjecture or guess to the questions ?
Center of mass system may be of your convenience.
Conservation of momentum:
$$p_1+ p_2 = p_1’+p_2’=0$$ for momentum vectors.
Conservation of energy:
$$KE_1+KE_2=KE’_1+KE’_2+Q$$ where Q is thermal energy generated by friction or inelasticity. Dashed means after collision or interaction.

 

[A.T.]

if I gave you a known projectile which you know everything about and told you to shoot it for me at x velocity, how would you change the wheel variables and why?

Why start a new thread, if you already have one open on this:
https://www.physicsforums.com/threa...l-launchers-like-tennis-ball-shooters.1066342

 

[Lnewqban]

while I know that friction and the normal force aren't dependent on surface area, I don't fully get it, wouldn't more surface area = more electrons pushing back = more friction/normal force?

if anyone spots information I missed please tell, and thank you.

You could use the concept of pressure here.
As the normal force or weight acting on the surface is the same, as the area of the contact surface becomes bigger, the pressure or force per unit of area decreases in the same proportion.
The value of the maximum possible static friction per unit of area decreases at the same rate as the area of the contact surface increases.

 

[cardboard_box]

Why start a new thread, if you already have one open on this:
https://www.physicsforums.com/threa...l-launchers-like-tennis-ball-shooters.1066342

as I have written in the old thread, I don't think I did a very good job of asking the question there. I am hoping that by starting this new thread it will be clearer what I am missing.

 

[cardboard_box]

You pose some questions. What are your own conjecture or guess to the questions ?
Center of mass system may be of your convenience.
Conservation of momentum:
$$p_1+ p_2 = p_1’+p_2’=0$$ for momentum vectors.
Conservation of energy:
$$KE_1+KE_2=KE’_1+KE’_2+Q$$ where Q is thermal energy generated by friction or inelasticity. Dashed means after collision or interaction.

my guess as to what is happening based on what I saw in similar systems is that the velocity of the contacting object (such as the wheel) coupled with friction exerts somehow exert a force on the object to accelerate/spin it.

as for your formulas my problem is that I am trying to find out what will happen without looking at the final state of the system or even the collision itself, but rather through knowing what every object's variable does try to predict how the final state of the system will be.

 

[cardboard_box]

You could use the concept of pressure here.
As the normal force or weight acting on the surface is the same, as the area of the contact surface becomes bigger, the pressure or force per unit of area decreases in the same proportion.
The value of the maximum possible static friction per unit of area decreases at the same rate as the area of the contact surface increases.

that's a pretty good explanation, I'll probably look around some more to make sure, but it workout intuitively, thanks.

 

[Lnewqban]

Look for an explanation of macroscopic characteristic of friction at this link:

https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/6-2-friction/

 

[anuttarasammyak]

my guess as to what is happening based on what I saw in similar systems is that the velocity of the contacting object (such as the wheel) coupled with friction exerts somehow exert a force on the object to accelerate/spin it.

That seems reasonable.

 

[cardboard_box]

Look for an explanation of macroscopic characteristic of friction at this link:

https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/6-2-friction/

in the article they mention that the model they use for friction does not work the same for objects at high velocities, do you have any source for me to read about high velocity affect on friction and what is considered high enough velocities? it seems like it might be the answer I am looking for since the wheel's RPM seems to determine projectile velocity aka the force exerted on it.

 

[cardboard_box]

That seems reasonable.

the problem is that it isn't truly, at least not at my level of understanding. since friction does not increase based on velocity and it isn't just a perfectly inelastic collision. the velocity that the wheel is spinning shouldn't at all determine the force exerted on an object, yet somehow it does.

 

[anuttarasammyak]

the problem is that it isn't truly, at least not at my level of understanding. since friction does not increase based on velocity and it isn't just a perfectly inelastic collision. the velocity that the wheel is spinning shouldn't at all determine the force exerted on an object, yet somehow it does.

Your conjecture is denied by your reasoning. Sad!

I like Kaiten Sushi https://en.wikipedia.org/wiki/Conveyor_belt_sushi. The dishes on the conveyor move with the same speed with no regard to their weight. It seems that your case be regarded as linear conveyer of very short length to me. May it be so ?

 

[cardboard_box]

Your conjecture is denied by your reasoning. Sad!

I like Kaiten Sushi https://en.wikipedia.org/wiki/Conveyor_belt_sushi. The dishes on the conveyor move with the same speed with no regard to their weight. It seems that your case be regarded as linear conveyer of very short length to me. May it be so ?

yes that is a perfectly inelastic collision, which I somewhat understand (still weird how it exerts a force to counter attempted motion even if the suhi plate itself isn't exerting a force or being exerted a force on by something else)

this model could somewhat work with 1 type of mechanism: the hooded flywheel shooter (assuming friction is static only of course) but it then implies that contact area should not matter at all, since the projectile simply "matches" the surface velocity of the wheel, which bothers me since especially for linear shooting mechanisms (2 wheels rotating in different directions and pushing the projectile between them) it really wouldn't matter how many wheels/contact area you got, which would mean a whole lot of the mechanisms built by very good robotics teams with a lot of information are simply wrong. and still, even in an hooded shooter configuration it feels like there must be a force rotating and pushing the projectile, otherwise it should just stick to the wheel and drag against the hood.

in addition what exactly would happen if instead of static friction it was kinetic? it should still somewhat exert a force on the object, granted here I am a bit more skeptical if velocity would change that exerted force.


btw I am just now aware that I am talking about a mechanism you may not understand, I can link some examples for a practical use if needed.

 

[A.T.]

the velocity that the wheel is spinning shouldn't at all determine the force exerted on an object, yet somehow it does.

Even if the force was the same, it would act for longer until the slipagge stops, so more momentum is transfered.

 

[A.T.]

still weird how it exerts a force to counter attempted motion even if the suhi plate itself isn't exerting a force or being exerted a force on by something else

That you find this weird indicates that you have some fundamental misconceptions about basic mechanics. You seem obsessed with naming 'causes' or 'sources of forces', instead of simply applying the laws and solving the equations.

 

[anuttarasammyak]

this model could somewhat work with 1 type of mechanism: the hooded flywheel shooter (assuming friction is static only of course)

Is it like the photo in https://en.wikipedia.org/wiki/Pitching_machine ?
Here just weight of ball is not enough to keep touching the roll. Ball is pinched and pressend between the roll and the hood to keep touching the roll. By putting the hood and ball inlet downside of the roll, where graivity jamms the ball to contact to the roll but the hood urges to do it, the machine could be used for "under throw" pitch.

 

[cardboard_box]

Even if the force was the same, it would act for longer until the slipagge stops, so more momentum is transfered.

I don't think I understand correctly what you mean, the projectile doesn't necessarily have to start while slipping against the wheel and then becomes static in relation to the wheel. and a faster wheel would push the ball out quicker, so contact time would be lesser.

 

[cardboard_box]

That you find this weird indicates that you have some fundamental misconceptions about basic mechanics. You seem obsessed with naming 'causes' or 'sources of forces', instead of simply applying the laws and solving the equations.

fair enough I am probably being unhealthily obsessed about the "sources". and sure, with the sushi plate it truly doesn't really matter. But with other examples such as the wheel and the projectile I just don't know what exact laws and equations are at play, and some things seem to contradict my observations about this types of mechanisms in the past.

 

[cardboard_box]

Is it like the photo in https://en.wikipedia.org/wiki/Pitching_machine ?
Here just weight of ball is not enough to keep touching the roll. Ball is pinched and pressend between the roll and the hood to keep touching the roll. By putting the hood and ball inlet downside of the roll, where graivity jamms the ball to contact to the roll but the hood urges to do it, the machine could be used for "under throw" pitch.

pretty much yes, the gravity part of your description I am not sure, since the shooter usually "raises" the ball with it while in contact (so the release angle is where the ball starts from in the picture you shared but the ball starts from further down). during contact the ball usually rolls against the wheel/hood too though.

 

[A.T.]

the projectile doesn't necessarily have to start while slipping against the wheel

In this machine it's unlikely that the surfaces move at the same velocities, when they come in contact. So you always start with slipping.

and then becomes static in relation to the wheel. and a faster wheel would push the ball out quicker, so contact time would be lesser.

You confuse the time of contact, with the time of acceleration. A slow wheel will accelerate the ball to its speed in shorter time, but the rest of the contact time is just wasted, with no further acceleration of the ball.

 

[russ_watters]

But with other examples such as the wheel and the projectile I just don't know what exact laws and equations are at play...

You were given instructions on how to solve the problem. Did you not understand them? I agree with A.T. here and think you should be trying to solve the problem instead of continuing these musings that don't seem to be leading anywhere.

 

[cardboard_box]

In this machine it's unlikely that the surfaces move at the same velocities, when they come in contact. So you always start with slipping.

You confuse the time of contact, with the time of acceleration. A slow wheel will accelerate the ball to its speed in shorter time, but the rest of the contact time is just wasted, with no further acceleration of the ball.

yes that makes sense, but that also means that the contact area of the wheel with the projectile just doesn't really matter, so with a linear shooter for example if i had another pair of wheels (that rotate at the same velocity as the original 2) it will do nothing if not harm the projectile velocity. while this definitely isn't a problem in terms of the physics, it clashes with what I saw from these systems in the past, that more contact time should help and with the intuition of "more wheel pushing = more velocity"

 

[cardboard_box]

You were given instructions on how to solve the problem. Did you not understand them? I agree with A.T. here and think you should be trying to solve the problem instead of continuing these musings that don't seem to be leading anywhere.

I don't recall being giving instructions on how to solve my problem, I was told that the overall momentum/KE of the system will remain the same but that isn't my problem. the problem isn't how given a wheel's initial state and wheel+projectile final state to find the energy transference but rather given projectile information and desired projectile final state what wheel design to choose, with the more specific and relevant problem to it being how velocity with friction determines the wheel velocity by exerting a force on it.

 

[russ_watters]

I don't recall being giving instructions on how to solve my problem, I was told that the overall momentum/KE of the system will remain the same but that isn't my problem. the problem isn't how given a wheel's initial state and wheel+projectile final state to find the energy transference but rather given projectile information and desired projectile final state what wheel design to choose, with the more specific and relevant problem to it being how velocity with friction determines the wheel velocity by exerting a force on it.

This is incoherently written and isn't a description of a physics problem.

I thought you were trying to calculate the final velocity of a ball given its size and mass and the mass and rpm of the wheel(s)? Are you hoping to build a ball launcher and need help designing it? What is the real end goal here?

Either way I think you need to organize your thoughts and clearly define what you really want to know. All these side questions about friction and such don't help move forward with solving the real problem (if there even is one). They are just distractions that don't seem to lead anywhere.

 

[cardboard_box]

This is incoherently written and isn't a description of a physics problem.

I thought you were trying to calculate the final velocity of a ball given its size and mass and the mass and rpm of the wheel(s)? Are you hoping to build a ball launcher and need help designing it? What is the real end goal here?

Either way I think you need to organize your thoughts and clearly define what you really want to know. All these side questions about friction and such don't help move forward with solving the real problem (if there even is one). They are just distractions that don't seem to lead anywhere.

the problem in general is "given certain projectiles and the wanted parameters for how to shoot them, pick a wheel set up" rather then "given certain projectiles and wheel set up determine the parameters"

I am aware (or at least think I am) of how the moment of inertia of the wheel and the torque the motor applies to the wheel will affect the system, but none of them determine final velocity, which is determined based on wheel RPM and is connected to friction of the wheel. that's what lead to the questions in this thread of how do we derive impact force from velocity/momentum (and other variables we need to know), since if there is momentum there must inherently be a potential to exert a force.

I think it is incoherent mainly because I am asking a question derived from another question but trying to make it more abstract and with an attempt at showing reasoning behind it so that I don't just make false assumptions and jump from there without the readers knowing.

So if you got any tips or insight on how to make my questions less incoherent for the future, please tell, since I get no joy from badly asking a question.

 

[anuttarasammyak]

the problem in general is "given certain projectiles and the wanted parameters for how to shoot them, pick a wheel set up" rather then "given certain projectiles and wheel set up determine the parameters"

The simple answer is
$$v=R\omega$$
where v is tangential speed of released projectile, R is radius and omega is angular velocity　of wheel.

 

[russ_watters]

First, please answer whether this is a real-world or hypothetical. Are you actually hoping to build one or just understand how they work?

[snipping and reorganizing]
So if you got any tips or insight on how to make my questions less incoherent for the future, please tell, since I get no joy from badly asking a question.

Please start with your writing; punctuation, capitalization, sentence structure. It will help us answer better if your writing is easier to understand. And it may well be that your writing is reflective of a disorganized thought process. So fixing one may help fix the other.

the problem in general is "given certain projectiles and the wanted parameters for how to shoot them, pick a wheel set up" rather then "given certain projectiles and wheel set up determine the parameters"

I think it is incoherent mainly because I am asking a question derived from another question but trying to make it more abstract and with an attempt at showing reasoning behind it so that I don't just make false assumptions and jump from there without the readers knowing.

What projectiles? What parameters? Being purposefully abstract makes things worse, not better. A coherent question/problem looks like this:

I have a uniform ball of radius r1 and mass m1 and a uniform wheel(single wheel launcher, free-spinning) of radius r2, mass m2 and thickness t. What rpm does the wheel need to spin to fire the ball at speed v?

A clear and specific question with an answer that can be expressed as an equation or calculated if numbers are added. Note, a single wheel launcher is more complicated than a two-wheel launcher because it spins the ball while launching it. It would probably be better to start with the easier case of the two-wheel launcher.

...but none of them determine final velocity, which is determined based on wheel RPM and is connected to friction of the wheel.

It is not connected(significantly) to the friction of the wheel. This can be calculated too, but first you should do the first problem, without it.

that's what lead to the questions in this thread of how do we derive impact force from velocity/momentum (and other variables we need to know), since if there is momentum there must inherently be a potential to exert a force.

Analyzing collisions like this does not depend on friction or force. You just need momentum before to calculate the momentum after, and knowing whether the collision is elastic or not. You can model a collision using force and deformation, but it is very complicated and doesn't change the answer. Adding-in dynamic friction gives a bit of loss, but it is small, and accounting for it would be very complicated. I highly doubt that anyone who actually designs these launchers considers it.

 

[cardboard_box]

First, please answer whether this is a real-world or hypothetical. Are you actually hoping to build one or just understand how they work?

I'd say hypothetical, I want to understand how they work (in order to be able to build one if needed but still mainly understand)

What projectiles? What parameters? Being purposefully abstract makes things worse, not better. A coherent question/problem looks like this:

I have a uniform ball of radius r1 and mass m1 and a uniform wheel(single wheel launcher, free-spinning) of radius r2, mass m2 and thickness t. What rpm does the wheel need to spin to fire the ball at speed v?

this is a bit tricky because like I said, I am mainly trying to understand the general usage rather then a specific case. but since you asked, here is a somewhat tricky example:
View attachment 1729619454025.webpyou need to shoot this torus , it has a 25 cm inside diameter, 36 cm outside diameter, 5 cm thickness and weights 255 grams.
and I want to shoot it at lets say 30 m/s preferably with spin. I need to shoot 1 every 8 seconds.
Here is the problem with the wheels: you are supposed to just choose or make your own wheels.
There isn't really guide on this part so I'm not sure how I can give info on this.

Analyzing collisions like this does not depend on friction or force. You just need momentum before to calculate the momentum after, and knowing whether the collision is elastic or not. You can model a collision using force and deformation, but it is very complicated and doesn't change the answer. Adding-in dynamic friction gives a bit of loss, but it is small, and accounting for it would be very complicated. I highly doubt that anyone who actually designs these launchers considers it.

as I hope I managed to show, this is the problem, you aren't given all the information but rather need to decide it on your own. so I can't know the final momentum because it is what I am solving for and neither can I know the impulse because it is determined by my choices during design.

 

[russ_watters]

and I want to shoot it at lets say 30 m/s preferably with spin. I need to shoot 1 every 8 seconds.
Here is the problem with the wheels: you are supposed to just choose or make your own wheels.
There isn't really guide on this part so I'm not sure how I can give info on this.

as I hope I managed to show, this is the problem, you aren't given all the information but rather need to decide it on your own. so I can't know the final momentum because it is what I am solving for and neither can I know the impulse because it is determined by my choices during design.

This sounds like a school project/design competition. But your goals seem to be contradictory: 30 m/s but "I can't know the final momentum because that's what I am solving for". Which is it? What other goals/constraints are there? This project seems really easy conceptually.

 

[cardboard_box]

But your goals seem to be contradictory: 30 m/s but "I can't know the final momentum because that's what I am solving for". Which is it?

I think I just made an extremely stupid assumption here that because I only know what momentum I *want* it to be rather then what it *will* be, I can't use final momentum.
I am honestly sorry for this.

What other goals/constraints are there? This project seems really easy conceptually.

the only other constraints/goals I can think of are that the shooter itself should be able to rotate around an axis and be able to choose lower velocities, but all of that isn't really a problem and could be solved quite easily.

as for the easy conceptually part, please elaborate, because to me it isn't that simple.
so here are some questions I have about this:
would you put your wheels on the top so they grip the top of the torus or on the sides?
what about opposing wheels such as on the bottom or other side?
how much would you choose to compress the torus*? (either from the side or from the top/bottom)
do you think contact area or contact time with the torus is at all important?
how much do you think spin will be important?

*since I can't give you any information about its elasticity just choose one that will work for you.

 

[Lnewqban]

in the article they mention that the model they use for friction does not work the same for objects at high velocities, do you have any source for me to read about high velocity affect on friction and what is considered high enough velocities? it seems like it might be the answer I am looking for since the wheel's RPM seems to determine projectile velocity aka the force exerted on it.

I am unable to find the mention you refer to in the article.
Could you guide me to it, please?

 

[cardboard_box]

I am unable to find the mention you refer to in the article.
Could you guide me to it, please?

"The equations given for static and kinetic friction are empirical laws that describe the behavior of the forces of friction. While these formulas are very useful for practical purposes, they do not have the status of mathematical statements that represent general principles (e.g., Newton’s second law). In fact, there are cases for which these equations are not even good approximations. For instance, neither formula is accurate for lubricated surfaces or for two surfaces siding across each other at high speeds. Unless specified, we will not be concerned with these exceptions."

seems to suggest kinetic friction (no idea if static friction too) acts differently then the formulas at high velocities. I don't know what is considered high enough velocity for it to apply and it is probably not very useful for my mechanism, but I am intrigued about this.

 

[Lnewqban]

"... For instance, neither formula is accurate for lubricated surfaces or for two surfaces siding across each other at high speeds..."

seems to suggest kinetic friction (no idea if static friction too) acts differently then the formulas at high velocities. I don't know what is considered high enough velocity for it to apply and it is probably not very useful for my mechanism, but I am intrigued about this.

Thank you for pointing that out.

I have found this article that describes the range of velocities that can cause changes in the molecular structure of the surfaces of metals, I believe:
https://www.sciencedaily.com/releases/2022/09/220906114220.htm

I also believe that your machine does not reach speeds of that magnitude.

 

[A.T.]

yes that makes sense, but that also means that the contact area of the wheel with the projectile just doesn't really matter

That is a weird reply to a post that had nothing to do with contact area, but was about velocity. You seem to be all over the place.

In any case, the simple model of friction, that is independent of velocity and contact area is just an approximation. It doesn't necessarily hold over arbitrarily large ranges of these variables, and for arbitrarily short interactions.

 

[cardboard_box]

That is a weird reply to a post that had nothing to do with contact area, but was about velocity. You seem to be all over the place.

yes, let me give a hopefully better example, if we are using a linear shooter (2 counter-rotating wheels and the projectile in the middle) then we add another set of wheels (fully identical to the first set with same RPM and everything). it really shouldn't matter at all to the final velocity of the projectile, that seems a little counter intuitive since there are more wheels pushing on the projectile. similarly it means you don't really need both wheels to "push" since it can't exceed maximum surface velocity anyways.

In any case, the simple model of friction, that is independent of velocity and contact area is just an approximation. It doesn't necessarily hold over arbitrarily large ranges of these variables, and for arbitrarily short interactions.

I doubt any mechanism in my range of building get to large enough velocities or contact areas for it to matter.