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

• B
• jaketodd
In summary: The bug has a very small mass, so it doesn't need to exert a large force to accelerate it to the same speed as the car. In summary, the bug may seem to be exerting a huge force on the car's windshield, but in reality it is only exerting a small force due to its extremely small mass. This is because the force of an object is dependent on its mass and acceleration, and the bug's small mass means it only needs to exert a small force to accelerate to the same speed as the car. This is why the windshield does not crack despite the bug hitting it at high speed.
jaketodd
Gold Member
...every body exerts an equal and opposite force, than what's put to it.

So, when I hit a bug in my car at 50 mph, why doesn't it crack my windshield?

This is probably a very basic question, with a very basic answer. I took high school physics, and also one physics class at college, but I have always wondered about this one.

F=ma so is it just that the bug has less mass than my car? But I still can't image it exerting the same force back, and not cracking my windshield.

Thanks

You seem to think that just because you are moving fast that you must hit something hard. Doesn't work that way. Imagine this. Hold up a sheet of paper and punch it as hard as you can. No big deal. Now go and punch the wall. (Don't really do that!) Do think that the forces exerted are the same?

But Newton's 3rd law doesn't care. Your fist and the sheet of paper exert the same (small) force on each other. Same with your windshield hitting that bug. And the wall and your fist -- same thing, but different forces involved.

hutchphd and russ_watters
Doc Al said:
You seem to think that just because you are moving fast that you must hit something hard. Doesn't work that way. Imagine this. Hold up a sheet of paper and punch it as hard as you can. No big deal. Now go and punch the wall. (Don't really do that!) Do think that the forces exerted are the same?

But Newton's 3rd law doesn't care. Your fist and the sheet of paper exert the same (small) force on each other. Same with your windshield hitting that bug. And the wall and your fist -- same thing, but different forces involved.
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?

jaketodd said:
But my windshield is exerting a huge force on that bug, not "(small)".
No, it isn't. That was my point.
jaketodd said:
So why doesn't the bug do that same to my windshield?
It does!

When things collide, the forces they exert on each other depend upon many factors. Such as mass, material, rigidity, and so on. But no matter what, the forces they exert on each other are equal and opposite.

The force on the bug isn't huge, but may well be enough to squish the bug. Your windshield doesn't even blink, the force is so low.

Dale
Ya but the force exerting on the bug is from my weight, and the weight of the whole car! So how can the bug equal that without cracking my windshield?

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

jaketodd said:
Ya but the force exerting on the bug is from my weight, and the weight of the whole car! So how can the bug equal that without cracking my windshield?
You should try calculating the force. Then you will see that it's tiny.
F=ma
So my car has an incredibly high amount of force.
You didn't calculate any forces. You're guessing. Do the math instead.

PeterDonis
jaketodd said:
So my car has an incredibly high amount of force.
This is conceptually wrong. Your car is able to potentially apply a large amount of force. For the bug however, it doesn't need to. It needs to accelerate the bug from stationary (as good as) to the velocity of the car in a very short time. So, ##F = ma## (Newton's second law), ##a##, the acceleration, is very large, but the mass ##m## is very small. As things turn out, the force required is small.

russ_watters
jaketodd said:
F=ma
So my car has an incredibly high amount of force.
If the bug gave that back, it would surely crack my windshield.
Note that is ##F = ma##, where ##a## is acceleration. It's not ##F = mv##, where ##v## is speed.

You can't equate force with speed directly.

PeterDonis and DaveE
For numbers: A fruit fly might weigh 0.1 milligrams, which is ##10^{-7}## kg. Let's say you drive about 100km/hr, which is rounded to 30 meters per second. Let's say you hit the fly and it accelerates from 0 to 30 meters per seconds in 0.01 seconds (so 10 milliseconds). Then the acceleration is 30m/s in 0.01 seconds is, on average, ##3000 m/s^2##. This is 300 times the acceleration of the Earth (300 g's, as it is often called) which is considerable I guess. So, what is the force? It is ##3000 * 10^{-7} = 0.0003 N##, which is tiny (in kilos it is 0.00003kg = 30 milligrams of force (I'm equation mass with weight here, I know, but it gives an idea) So that is a tiny force...

russ_watters
So the bug has so little mass, that decelerating it is no big task for a windshield? I just think it's deceptive to say that every force exerted on another, returns the same force. But I guess it makes sense when the relative masses are taken into effect with F=ma.

Why is that deceptive? The windshield only needs to apply round about 30 milligrams of force to accelerate the bug from 0 to 100 km/h. That is exactly the force that the but also applies to the windshield. Nothing deceptive there I would say.

russ_watters
jaketodd said:
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?
jaketodd said:
Ya but the force exerting on the bug is from my weight, and the weight of the whole car! So how can the bug equal that without cracking my windshield?
You should look at it in reverse to help visualize it: The bug hits the car and exerts a small force on it and the car responds with the same small force.

The car cannot hit the bug harder than the bug can hit the car.

jaketodd said:
F=ma
So my car has an incredibly high amount of force.
##F=ma## kind of gives you hint: Does your car decelerate when you hit a bug (or a bug hits your car if you prefer)?

No, it doesn't. Thus the acceleration ##a## must be very close to zero (no change in velocity) and it follows that the force ##F## must also be very close to zero.

PeterDonis, valenumr, russ_watters and 2 others
jack action said:
The car cannot hit the bug harder than the bug can hit the car.
This is exactly what it comes down to

I think you might be confused about some basic concepts, like velocity, acceleration, force, impulse (force x time). I'm not sure our words will suffice to clarify this without some studying of the basics. Like how an applied force relates to an object's velocity.

This is an important foundation to this problem. If you analyse it carefully, it's not as simple as it sounds. The truth is we don't actually know what the instantaneous force is on the bug. That depends on the details of how the bug smashes with time. Kind of like a spring compressing, but not as reversible. So, the concept of impulse is really useful here, it allows us to ignore the force details vs. time and focus on the total change in velocity from before to after. This also relates to the ability of the windshield to withstand the collision.

I would first focus on problems like solid objects colliding and the calculations about how "before" is different than "after". These will be common in physics courses and online resources.

You are also overestimating the stiffness of the bug. Compare it to a stone. You can crush the bug between your fingers, but not the stone. That is why a stone might crack your windshield.

jaketodd, PeroK and russ_watters
I suggest the following method to estimate bug smashing force:

1) From the bug size and mass, calculate the size of a cylinder of water with the same length and mass as the bug.
2) Since it makes no difference if the windshield moves toward the bug, or the bug toward the windshield, assume the cylinder of water is moving toward the windshield.
3) To make it easier, assume it hits the windshield at 90 degrees (perpendicular).
4) Now use Bernoulli's equation: ##\Delta P = 0.5\rho V^2## to calculate the velocity pressure of the "bug".
5) Multiply by the cross sectional area of the bug simulation water cylinder to get force.
6) Feel free to include the windshield angle in the calculation.

This should work reasonably well for bugs large enough to splatter, such as dragonflies. And not so well for small bugs with strong exoskeletons, such as mosquitoes.

That sounds way too advanced for the order of magnitude we are after here. I estimated very roughly 0.3 milliNewton of force. Maybe I'm a whole order of magnitude off, then you have 3 milliNewton, that's still nothing...

russ_watters and Frabjous
Or is it the bug cannot hit the car less than the car can hit the bug? =)

Arjan82
jaketodd said:
Or is it the bug cannot hit the car less than the car can hit the bug? =)
Actually, that's a good way to look at it. The collision can be viewed equally from the frame of reference in which the car is moving at 50mph or the frame of reference in which the bug is moving at 50mph and the car is at rest. The physics and the outcome are equivalent in both frames.

The question is: how fast would a bug need to be moving in order to shatter the windscreen? The answer is a lot more than 50 mph.

PeroK said:
Actually, that's a good way to look at it. The collision can be viewed equally from the frame of reference in which the car is moving at 50mph or the frame of reference in which the bug is moving at 50mph and the car is at rest. The physics and the outcome are equivalent in both frames.

The question is: how fast would a bug need to be moving in order to shatter the windscreen? The answer is a lot more than 50 mph.
Well sure, common sense tells you that a little bug is not going to be like a head on crash. But if the forces are equal and opposite... just a confusing way to word it I think, Mr. Newton. Or Sir Newton, sorry I forgot your title, haha!

jaketodd said:
Well sure, common sense tells you that a little bug is not going to be like a head on crash. But if the forces are equal and opposite... just a confusing way to word it I think, Mr. Newton. Or Sir Newton, sorry I forgot your title, haha!
Sir Isaac is the term of address you're looking for if you want to stand on ceremony.

PeterDonis and jaketodd
jaketodd said:
...every body exerts an equal and opposite force, than what's put to it.

So, when I hit a bug in my car at 50 mph, why doesn't it crack my windshield?

This is probably a very basic question, with a very basic answer. I took high school physics, and also one physics class at college, but I have always wondered about this one.

F=ma so is it just that the bug has less mass than my car? But I still can't image it exerting the same force back, and not cracking my windshield.

Thanks
If I understood it correctly then as you hit the bug it will not break the windshield because as you, your fist and bug is moving with 50mph wind shield is too. When you apply force it’s your force on the bug that matters. When it hits the windshield , the windshield just experiences this force not some kind of force added with the force due to speed of the car. So it’s little force. It can not break it. But if you try hard you can break it with your fist.
On the contrary if the wind shield is stationary then it can break as the bug will act like a Bullet.

jack action and PeroK

I just think the "equal and opposite force" wording can be easily misinterpreted and lead to confusion with people trying to understand it.

jaketodd said:
Not everyone!

jaketodd said:
I just think the "equal and opposite force" wording can be easily misinterpreted and lead to confusion with people trying to understand it.
There's no other way to describe it. It's fairly pointless complaining that Newton's laws might be misunderstood. Anything can be misunderstood.

Let me give you an example. The movies are full of people punching each other in the face. And, with a few exceptions, no one every hurts their hand. But, it's difficult to punch someone hard in the head without hurting your hand.

So, you might side with the film directors and assume that the person getting punched will be hurt, but the person doing the punching will not. Because neither you nor they understand Newton's third law.

But, Newton knew more than film directors. He knew that however hard you punch someone, your fist gets the same treatment.

In fact there was a case recently in the World 20-20 cricket semi-final where a New Zealand batsman got out and was so annoyed he punched his bat, broke a finger and missed the final, which NZ lost. Now, if he had paid attention in his physics classes, he might have played in the final, and might even have helped NZ beat Australia!

vanhees71
PeroK said:
In fact there was a case recently in the World 20-20 cricket semi-final where a New Zealand batsman got out and was so annoyed he punched his bat, broke a finger and missed the final, which NZ lost. Now, if he had paid attention in his physics classes, he might have played in the final, and might even have helped NZ beat Australia!
There is hope for Indians too.

jaketodd said:
I just think the "equal and opposite force" wording can be easily misinterpreted and lead to confusion with people trying to understand it.
The problem is not this wording, but you confusing force with damage.

sophiecentaur, vanhees71, russ_watters and 1 other person
A.T. said:
The problem is not this wording, but you confusing force with damage.
Or velocity.

jaketodd said:
Ok man
We're trying to help. The statement you are saying is confusing is basically 1=1. It's hard to see how that could be confusing unless you think it means something else.

In a prior post you said the car "has a force" which implies to me you think force is a property of the car that doesn't depend on its interactions. Hits a bug, has a force = x. Hits another car, same force x. Hopefully by now you recognize that the mutual interaction causes the force; it wasn't there before the interaction.

PeterDonis, vanhees71, jack action and 2 others
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.

sophiecentaur, russ_watters, DaveE and 1 other person
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.

PeterDonis, rudransh verma, vanhees71 and 1 other person
Cool, thanks All

russ_watters
jaketodd said:
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.

Mister T said:
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.

russ_watters

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