Greater momentum on impact means greater force?

[dibbsy]

OK, but how does that explain why the faster car does the greater damage? No closer to a solution as far as I can see, unless we leave change of velocity right out of it and focus on force varying with kinetic energy. Surely this has been understood since Newton? What am I missing here?

 

[Frabjous]

OK, but how does that explain why the faster car does the greater damage? No closer to a solution as far as I can see, unless we leave change of velocity right out of it and focus on force varying with kinetic energy. Surely this has been understood since Newton? What am I missing here?

The magnitude of the force is roughly proportional to Δv. Δv is equal to the initial velocity of the car. So a faster car generates a larger force. A larger force generates a larger stress (defined in an earlier post) which causes more damage.

 

[dibbsy]

Sure, but this has nothing to do with acceleration! The Delta V here is the difference between the V of the slower car and the V of the faster car, both of which are travelling inertially. Given that, then what you say is fine and completely consistent with what I'm saying: in the inertial case it's all about Delta mv^2, not Delta V/Delta T since there is no Delta T

 

[Frabjous]

Acceleration is fundamentally about changes in velocity.

The Delta V here is the difference between the V of the slower car and the V of the faster car, both of which are travelling inertially. Given that, then what you say is fine and completely consistent with what I'm saying: in the inertial case it's all about Delta mv^2, not Delta V/Delta T since there is no Delta T

No it is not. There are two Δv's, one for the fast car and one for the slow car. I gave you an equation with a Δt and it confused you, so I simplified further.

 

[256bits]

not Delta V/Delta T since there is no Delta T

You ever run, play softball and slide into second base, ride a bicycle.
How do you ever slow down to a stop?
Certainly not instantaneously.
The slowing down is called deceleration ( which can be called negative acceleration ).
There is a change in speed, in a certain time period.

A car crash is the same thing, except the change in speed happens much quicker.
the deceleration ( negative acceleration ) can be in milliseconds.

 

[dibbsy]

Acceleration is fundamentally about changes in velocity.No it is not. There are two Δv's, one for the fast car and one for the slow car. I gave you an equation with a Δt and it confused you, so I simplified further.

The equation you gave does not explain what I'm wanting explained. As I said, there is no acceleration, so the greater force of the faster car cannot be explained by acceleration. Simple as that.

 

[dibbsy]

You ever run, play softball and slide into second base, ride a bicycle.
How do you ever slow down to a stop?
Certainly not instantaneously.
The slowing down is called deceleration ( which can be called negative acceleration ).
There is a change in speed, in a certain time period.

A car crash is the same thing, except the change in speed happens much quicker.
the deceleration ( negative acceleration ) can be in milliseconds.

OK, but nothing you have said explains why the faster car causes the greater damage! How could deceleration possibly explain this?

 

[Ibix]

The point you seem to be missing (or, more accurately, vigorously denying) is that there is acceleration: the car comes to a stop (or at least slows down if the wall is flimsy). And if the car is initially going faster the acceleration will be larger.

 

[dibbsy]

Sorry, but don't you see how absurd that sounds? If the car is going faster, the deceleration is larger. Call it 'negative acceleration' if you like, but it no more explains the larger force than my going backwards faster than you explains any damage to what is in front of me. Absurd!

 

[weirdoguy]

Sorry, but don't you see how absurd that sounds?

You clearly do not understand what acceleration is. Change in velocity means there is acceleration, per definition.

 

[Frabjous]

Sorry, but don't you see how absurd that sounds? If the car is going faster, the deceleration is larger. Call it 'negative acceleration' if you like, but it no more explains the larger force than my going backwards faster than you explains any damage to what is in front of me. Absurd!

Then you have no understanding of what F=ma means.

We are not sitting across a table from one another. Forum communications are much more limited. Given this, you will be better served by trying to figure why we are right, not by trying to have us refute your position.

I am tapping out.

 

[Ibix]

Sorry, but don't you see how absurd that sounds? If the car is going faster, the deceleration is larger. Call it 'negative acceleration' if you like, but it no more explains the larger force than my going backwards faster than you explains any damage to what is in front of me. Absurd!

Do recall when describing things as "absurd" that you are talking about the principles of physics used to design and build the car in the first place. There are literally thousands of pieces of hard evidence around you that those principles are not absurd, however you might feel.

You yourself quoted that force is mass times acceleration, so you presumably accept that there's a force now you accept that there's an acceleration. The reason that the force has a negative sign is that it's pointing in the opposite direction to the car's motion - from the wall into the car. That's why the car crumples and slows.

Now remember Newton's third law. We've been talking about the force on the car, but the car exerts an equal and opposite force on the wall. That's the one that does the damage to the wall.

 

[weirdoguy]

Assuming that time of collision is roughly the same you have
$$F_1=m\frac{\Delta v_1}{\Delta t},
F_2=m\frac{\Delta v_2}{\Delta t}$$
If $\Delta v_1>\Delta v_2$ then $F_1>F_2$.

Why LateX is not working?
EDIT: it works now, yay.

 

[Ibix]

Why LateX is not working?

You're the first to use it on this page. Refresh and it'll be fine.

 

[dibbsy]

You clearly do not understand what acceleration is. Change in velocity means there is acceleration, per definition.

No, change in velocity can be acceleration or deceleration. Direction actually matters. I still do not see how, if A decelerates into W with greater magnitude than B decelerates into W, that explains why A does greater damage to W than B does. It has to be about kinetic energy, not deceleration.

 

[dibbsy]

Then you have no understanding of what F=ma means.

We are not sitting across a table from one another. Forum communications are much more limited. Given this, you will be better served by trying to figure why we are right, not by trying to have us refute your position.

I am tapping out.

LOL I appreciate all your efforts, but tbh you're not all saying the same thing and I don't think you have a collective explanation of 'why you are right' and I have not seen an actual explanation from any one of you! I'm about to tap out too, but I appreciate the responses anyhow

 

[weirdoguy]

can be acceleration or deceleration

Sigh. It's the same, acceleration is a vector, so it has direction built in it. I see no point in using term "deceleration". It changes nothing in what I said. I proved that force is larger for larger speed.

 

[weirdoguy]

but tbh you're not all saying the same thing

We are. You just don't understand what acceleration is.

 

[dibbsy]

Do recall when describing things as "absurd" that you are talking about the principles of physics used to design and build the car in the first place. There are literally thousands of pieces of hard evidence around you that those principles are not absurd, however you might feel.

I did not say the principles of physics are absurd. I'm asking what the principle is that explains why the faster car does the greater damage.

You yourself quoted that force is mass times acceleration, so you presumably accept that there's a force now you accept that there's an acceleration. The reason that the force has a negative sign is that it's pointing in the opposite direction to the car's motion - from the wall into the car. That's why the car crumples and slows.

Well, the wall is not accelerating into the car, so I don't quite get that. But anyhow, I'm not asking why the car crumples and slows. I'm asking why the faster car does the greater damage to the wall!

Now remember Newton's third law. We've been talking about the force on the car, but the car exerts an equal and opposite force on the wall. That's the one that does the damage to the wall.

Ah yes, if you scroll back up I proposed much earlier that maybe the Third Law is what explains the damage to the wall. But it seems to me that it is circular to appeal to the Third Law, because that assumes that negative acceleration is what explains the damage to the car by the wall. But I'm questioning in the first place whether acceleration has anything to do with it! I'm saying that it's about more kinetic energy in the faster car. So it exerts greater force on the wall than the slower car and so damages the wall more. No need for the Third Law except to explain why the wall also damages the car.

 

[weirdoguy]

I'm asking why the faster car does the greater damage to the wall!

I've answered that here:

Assuming that time of collision is roughly the same you have
$$F_1=m\frac{\Delta v_1}{\Delta t},
F_2=m\frac{\Delta v_2}{\Delta t}$$
If $\Delta v_1>\Delta v_2$ then $F_1>F_2$.

+ third Newton's third law, car exerts the same (in magnitude) force on wall as wall on the car.

 

[dibbsy]

Sigh. It's the same, acceleration is a vector, so it has direction built in it. I see no point in using term "deceleration". It changes nothing in what I said. I proved that force is larger for larger speed.

Sorry I still don't get it. I have assumed no acceleration by the car. Make it even clearer: the two cars are perfectly rigid and uncollapsible. The walls are made of cheese. The faster car will do more damage to the cheese wall than the slower car, with no acceleration or deceleration whatsoever. It's the kinetic energy that does the damage - more forward energy into the wall, more damage. What's acceleration got to do with it??

 

[weirdoguy]

I have assumed no acceleration by the car.

If there is no acceleration then it can't stop. No acceleration=no change in speed or veloccity.

with no acceleration or deceleration whatsoever.

Nonsense! Speed changes, so acceleration is non-zero!

 

[dibbsy]

I've answered that here:
+ third Newton's third law, car exerts the same (in magnitude) force on wall as wall on the car.

See my post below. I don't think the Third Law does the trick.

 

[weirdoguy]

I don't think the Third Law does the trick.

Then what you think is wrong.

 

[dibbsy]

If there is no acceleration then it can't stop. No acceleration=no change in speed or veloccity.
Nonsense! Speed changes, so acceleration is non-zero!

See my other post. The walls can be made of candy floss, the cars made of titanium. No acceleration, no deceleration. The larger kinetic energy of the faster car will do more damage to the wall than the lower kinetic energy of the slower car. What's incorrect about that?

 

[dibbsy]

Then what you think is wrong.

I say it's all about the kinetic energy. Nothing to do with acceleration or the Third Law. How is this incorrect as far as physics goes??

 

[weirdoguy]

How is this incorrect as far as physics goes??

I have showed you how by explicitly wirting out Newton's second law which included acceleration. I can't do more than that. You have basic misunderstandings about what acceleration is.

 

[Ibix]

I say it's all about the kinetic energy. Nothing to do with acceleration or the Third Law. How is this incorrect as far as physics goes??

Transfer of energy is the work done, which is the force applied times the distance moved. If there's no force then there's no energy transfer.

Looking at energy transfer is another way of looking at the force, or the integral thereof. It's maybe an easier way to look at it, but the force method tells you exactly the same thing.

No time to reply to your answer to my last right now.

 

[dibbsy]

I have showed you how by explicitly wirting out Newton's second law which included acceleration. I can't do more than that. You have basic misunderstandings about what acceleration is.

You still haven't shown how what I said is wrong.

 

[dibbsy]

Transfer of energy is the work done, which is the force applied times the distance moved. If there's no force then there's no energy transfer.

Looking at energy transfer is another way of looking at the force, or the integral thereof. It's maybe an easier way to look at it, but the force method tells you exactly the same thing.

No time to reply to your answer to my last right now.

OK, so then why not conclude that the greater force of the faster car comes from the greater kinetic energy? The transfer comes from the impact. The impact involves a force. The greater the kinetic energy, the greater the force that is transferred. No mention of acceleration.

 

[malawi_glenn]

No, change in velocity can be acceleration or deceleration.

Deceleration is just a fancy word for "acceleration that decreases the speed"

Consider circular motion with constant speed. But the velocity is changing at every instant because the direction is changing. What should we call this effect? It is not changing speed...

https://www.vedantu.com/formula/deceleration-formula
It is more of an informal concept, perhaps that is why you are confused?
(in my country, we say things like the velocity limit on roads, etc. Which is wrong but it is common saying).

Acceleration is rigorously defined as (a vector) $\displaystyle \vec a = \lim_{\Delta t \, \to \, 0}\dfrac{\Delta \vec v}{\Delta t}$

Tip: try to unlearn the concept deacceleration, it does no good

 

[Mister T]

Sorry, but don't you see how absurd that sounds? If the car is going faster, the deceleration is larger. Call it 'negative acceleration' if you like, but it no more explains the larger force than my going backwards faster than you explains any damage to what is in front of me. Absurd!

The word decelerate is confusing you. Any time you speed up, slow down, or change direction you are accelerating.

To decelerate means to decrease speed. This has nothing to do with whether the acceleration is positive or negative.

 

[jbriggs444]

OK, so then why not conclude that the greater force of the faster car comes from the greater kinetic energy? The transfer comes from the impact. The impact involves a force. The greater the kinetic energy, the greater the force that is transferred. No mention of acceleration.

Force is not something that is transferred. A force is a transfer of momentum. The thing that is transferred is momentum, not force.

When you transfer momentum to something then, in the absence of other competing effects, the result is an acceleration. That is Newton's second law: $\sum F = ma$.

The transfer of kinetic energy is through a quantity known as "work". This can be numerically calculated as force multiplied by displacement in a direction parallel to the applied force: $W = F \cdot s$.

Yes, if the car is perfectly rigid, comes to rest and does not rotate as a result of the collision then all of the kinetic energy is lost by the car and will manifest as work done by the car on the wall.

Yes, the work done on the wall by the car will be energy gained by the wall. If the wall remains roughly at rest following the collision so that its bulk kinetic energy remains zero, this energy will have to be absorbed or dissipated somehow.

Yes, if the wall has no elasticity or resiliency so that the energy cannot be stored as vibrations then the energy will go into permanent deformation, breakage and thermal energy.

I believe that there is a rough proportionality -- the greater the absorbed energy is per unit mass, the more finely divided the rubble will be. More energy = more rubble or a more powdery residue.

My understanding is that one of the ways that kinetic energy was first studied was by looking at the variation in the size of impact craters in mud versus fall distance. This is a better scenario to study than cars crashing into walls. Cheaper, easier, more measurable.

 

[zdcyclops]

OK so the cars are slowed when they hit the wall. That means they decelerate. The faster the car's velocity, the greater the deceleration needed to slow it down, so the greater the force needed to slow it down. So how does that explain the greater damage done to the wall by the faster car?

Acceleration and deceleration are the same thing. There is no time variable in the equation. Acceleration is the velocity. Reverse the equation m x a = F

 

[weirdoguy]

Acceleration is the velocity

What?