B According to Newton's 3rd Law....

[jbriggs444]

There are different ways to state Newton's third law.

A "force" can be understood as one important aspect of an interaction between two objects. It tells you how fast momentum is being transferred from one object to the other.

Large force: Large rate of change of momentum.
Small force: Small rate of change of momentum.

That is pretty much the second law. $F=ma$ and $ma$ is the rate of change of momentum (as long as mass is not changing).

The third law asserts that the rate at which momentum is increasing in the one object (the force of A on B) matches the rate at which momentum is decreasing in the other (the additive inverse of the force of B on A). It is essentially a statement that all interactions conserve momentum.

 

[Chestermiller]

The force your windshield exerts on a bug is equal in magnitude to the force the bug exerts on your windshield. But the force required to squash a bug is much less than the force required to crack a windshield. It is a "materials" issue (i.e., the amount of force required to cause a given material fo fail). This is called the strength of the material.

 

[jaketodd]

Cool, thanks All

 

[Herman Trivilino]

But my windshield is exerting a huge force on that bug, not "(small)". So why doesn't the bug do that same to my windshield?

No, the bug undergoes a much much larger acceleration than the windshield. Because of its much much small mass. You are confusing force with the effect of a force. The effect is measured by the acceleration.

 

[PeroK]

No, the bug undergoes a much much larger acceleration than the windshield. Because of its much much small mass. You are confusing force with the effect of a force. The effect is measured by the acceleration.

If you already had a live bug on the windscreen and it was the point of contact with the bug hit by the car, then both bugs would be squashed, despite the windscreen bug undergoing far less acceleration than the flying bug.

 

[jaketodd]

I think it's about materials. A pebble, with the same mass as the bug, would crack my windshield. In fact, I have cracks in my windshield from probably pebbles from the truck in front of me.

 

[Arjan82]

probably not though. A pebble with the same mass as the bug is a sand grain. That wouldn't crack your windshield at all.

 

[jaketodd]

Ok, imagine driving at 50 mph through a sandstorm. Wouldn't that mess up your windshield?

 

[jbriggs444]

Ok, imagine driving at 50 mph through a sandstorm. Wouldn't that mess up your windshield?

At some speed, certainly. Sandblasting clear glass will produce frosted glass.

I've never tried low velocity sandblasting with beach sand to see whether it succeeds in frosting laminated safety glass. My untutored feeling is that there is a minimum velocity beneath which the impacts are elastic and non-damaging.

 

[jaketodd]

Elastic. So it does come down to materials science?

 

[valenumr]

F=ma
So my car has an incredibly high amount of force.
If the bug gave that back, it would surely crack my windshield.

You're car would generally have momentum, not force. As does the bug. When the bug hits the windshield, it decelerates very rapidly (this is basically an impulse force, or more thoroughly an elastic collision). The question you should ask is: how much does your car (or windshield) decelerate? It is negligible because the car is massive compared to the bug.

 

[jaketodd]

If it's momentum, not force, then why does Newton say equal and opposite force? You guys are the experts. And I believe you. Just a confusing way of wording it I think - equal and opposite force. It conjures ideas of the bug hitting your windshield with as much force as the car hitting it - like a head on collision with a car of equal mass, except it's a bug doing it.

 

[PeroK]

You're car would generally have momentum, not force. As does the bug. When the bug hits the windshield, it decelerates very rapidly (this is basically an impulse force, or more thoroughly an elastic collision). The question you should ask is: how much does your car (or windshield) decelerate? It is negligible because the car is massive compared to the bug.

That idea was debunked just a few posts ago!

 

[PeroK]

You guys are the experts.

Not everyone is an expert and everyone makes mistakes. You still need to exercise judgement over what is posted on here.

Even the "Science Advisor" badge does not make us immune from error.

 

[valenumr]

If it's momentum, not force, then why does Newton say equal and opposite force? You guys are the experts. And I believe you. Just a confusing way of wording it I think - equal and opposite force. It conjures ideas of the bug hitting your windshield with as much force as the car hitting it - like a head on collision with a car of equal mass, except it's a bug doing it.

Force is equal to mass times acceleration (F = m*a). Momentum is mass times velocity (p =m*v) If you consider acceleration is change of velocity with respect to time (a = dv/dt), you can work out that force is also equivalent to change in momentum with respect to time. So I was just trying to clarify that your car doesn't necessarily have a pre-existing "force" if it is moving at a constant velocity, but it can still impart a force (change of momentum) on the bug, because the car has momentum with respect to the bug.

 

[Nugatory]

Elastic. So it does come down to materials science?

When we are analyzing the details of energy transfer in inelastic collisions (ones in which some of the kinetic energy is spent cracking, breaking, squashing, heating, deforming, spattering things like bugs and windshields) then yes, the characteristics of the materials involved are important.

However, we don’t get to that level of analysis until after we have a solid understanding of Newton’s laws and how they are always at work. The details of the collision make it harder to calculate the forces between the two bodies, but these forces are always equal and opposite by Newton’s third law.

 

[Doc Al]

If it's momentum, not force, then why does Newton say equal and opposite force? You guys are the experts. And I believe you. Just a confusing way of wording it I think - equal and opposite force. It conjures ideas of the bug hitting your windshield with as much force as the car hitting it - like a head on collision with a car of equal mass, except it's a bug doing it.

It seems like you're still not getting Newton's 3rd law. The bug does hit the windshield with exactly the same force (opposite direction, of course) as the windshield exerts on the bug. Really!

 

[Nugatory]

It conjures ideas of the bug hitting your windshield with as much force as the car hitting it

Which is exactly what happens if you do the calculation.

We can start with a car of mass $M$ moving with speed $v$. It strikes a hovering bug of mass $m$, the bug is duly squashed and sticks to the windshield. Let’s say the collision takes some very small time $\Delta T$ (for reasonable assumptions about the speeds and masses $\Delta T$ will be a few tens of microseconds, consistent with our experience that the time to squash the bug is much less than human reflex time).

So now we have a car-plus-bugpulp with a mass of $M+m$ moving down the road. What is its speed? By conservation of momentum it is $v’=v\frac{M}{M+m}$ (which for reasonable assumptions about the masses of bugs and cars is different from $v$ by an almost undetectably small amount, which is why your intuition is leading you astray).

OK, so the bug of mass $m$ was accelerated from zero to $v’$ by the force of the car on the bug. What force, acting for time $\Delta T$ on the mass $m$, will produce that change in speed? We can calculate it and call it $F_{CB}$.

The car is decelerated from speed $v$ to $v’$ by the force of the bug on the car. What force, acting for time $\Delta T$ on the mass $M$, will produce that speed? We can calculate it and call it $F_{BC}$.

Do the algebra and we will find that $F_{CB}=-F_{BC}$ - the force of bug on windshield is equal to force of windshield on bug, as Newton promised.

(Note that I have simplified the calculation by ignoring the tiny amount of kinetic energy that was spent turning the bug into bug pulp. You can include if you want - by $W=Fd$ it will be roughly equal to the size of the bug times $F_{CB}$ - but if you do you’ll just see why I’m justified in ignoring it)

 

[PeterDonis]

I have simplified the calculation by ignoring the tiny amount of kinetic energy that was spent turning the bug into bug pulp.

I don't think you actually have to ignore anything in your computation since you are computing conservation of momentum, not conservation of energy. In other words, you are not assuming an elastic collision, since momentum is conserved whether the collision is elastic or inelastic (which this collision is).

If you were to compute energy conservation, then there would be a (tiny) term due to the inelasticity of the bug that you could ignore for most purposes.

 

[DaveE]

If it's momentum, not force, then why does Newton say equal and opposite force? You guys are the experts. And I believe you. Just a confusing way of wording it I think - equal and opposite force. It conjures ideas of the bug hitting your windshield with as much force as the car hitting it - like a head on collision with a car of equal mass, except it's a bug doing it.

Because it's not momentum, it's the rate of change in momentum. There's a big difference. Newton just used the common name for the rate of change of momentum. Reread this:

There are different ways to state Newton's third law.

A "force" can be understood as one important aspect of an interaction between two objects. It tells you how fast momentum is being transferred from one object to the other.

Large force: Large rate of change of momentum.
Small force: Small rate of change of momentum.

That is pretty much the second law. F=ma and ma is the rate of change of momentum (as long as mass is not changing).

The third law asserts that the rate at which momentum is increasing in the one object (the force of A on B) matches the rate at which momentum is decreasing in the other (the additive inverse of the force of B on A). It is essentially a statement that all interactions conserve momentum.

 

[Nugatory]

"The wording is fine and cannot be blamed for your misguided ideas."

Ya that's really constructive.

That’s fair, but I still have to ask: if you don’t like the wording, what might be a better way of stating Newton’s third law?

 

[PeterDonis]

It conjures ideas of the bug hitting your windshield with as much force as the car hitting it - like a head on collision with a car of equal mass, except it's a bug doing it.

But a bug doing it is not the same as a car of equal mass doing it at the same relative speed. That's the whole point. Force is not mass alone, it's mass times acceleration. If a bug hits your windshield, the bug decelerates a lot, but its mass is tiny; the car has a large mass, but a tiny deceleration. The result is a tiny force--the same tiny force both ways.

If, OTOH, two cars of equal mass collide, both of them decelerate a lot. It's the large mass times the large deceleration that makes the force much larger--much larger both ways.

 

[rudransh verma]

@jaketodd The windshield is moving too at 50 mph because it’s attached to the car. So it doesn’t make any difference whether it’s 50 or 500. All that matters is your force on bug which is very less to break a windshield. It’s that simple.
It doesn’t matter if it’s moving car or stationary ground.

 

[valenumr]

That idea was debunked just a few posts ago!

Oh gosh, I can see how this might be confusing the way it is written. I wasn't referring to the collision. I was referring to the properties of the car before the collision.

 

[PeroK]

Oh gosh, I can see how this might be confusing the way it is written. I wasn't referring to the collision. I was referring to the properties of the car before the collision.

A pebble can shatter the windscreen, but it's not going to slow the car down significantly.

 

[jbriggs444]

A pebble can shatter the windscreen, but it's not going to slow the car down significantly.

Spark plug fragments can do a number on the tempered glass in side windows.

As I understand it, tempered safety glass is pre-stressed. All it takes is the creation of a tiny flaw for those stresses to shatter the remainder of the window. The ceramic in a shattered spark plug is hard enough and has edges sharp enough to create such a flaw.

 

[jaketodd]

That’s fair, but I still have to ask: if you don’t like the wording, what might be a better way of stating Newton’s third law?

I really don't know. You guys are the experts, and it seems a conclusion hasn't been reached yet. Maybe Newtons 3rd Law should be introduced or worded with caveats like the ones we see in this thread.

 

[Nugatory]

I really don't know. You guys are the experts, and it seems a conclusion hasn't been reached yet. Maybe Newtons 3rd Law should be introduced or worded with caveats like the ones we see in this thread.

What caveats? The force of the bug on the windshield and the force of the windshield on the bug are exactly equal and opposite with no ifs, ands, buts or other hedging. That has been stated explicitly and repeatedly, starting with the very first reply you received and most recently in posts #47, #48, and following.

All the other discussion has been about why these equal and opposite forces can produce very different impact effects and why you are therefore mistaken to assume from the different effects that the forces are different.

 

[Nugatory]

This thread is closed as the discussion is no longer productive.

As with all such thread closures, if you feel that there is something to say that has not already been said, you can PM me or any of the mentors and we can reopen it for your contribution.