Greater momentum on impact means greater force?

[berkeman]

visualizing a car crumpling

Sorry about your car.

 

[hutchphd]

Although (to contradict myself in #29) I think some of the force limiters in F1 cars don't become effective until higher speeds (tires shear off and some crumple zones only at high force). And when I used to downhill ski the bone-breaking accidents were often the slow speed ones because the bindings didn't release. So just don't run into into stuff.

 

[dibbsy]

The car experiences a change of velocity Δv in a time Δt. The force is then $F=m {\frac {\Delta v}{\Delta t} }$. Δv is obviously larger. Δt is smaller because things are happening faster. So the force is larger.

Sorry, I don't understand that at all.

 

[dibbsy]

You've got some funny ideas, if you don't mind my saying.

There's an old joke that if you jump off a tall building it's not the fall that kills you ... but when you hit the ground.

But, actually, it's not hitting ground that kills you ... it's what happens after you hit the ground.

Sorry, after you hit the ground the damage has already begun! Nothing funny about that idea, if you don't mind my saying ;-)

 

[Frabjous]

Sorry, I don't understand that at all.

Think of it as an average force. The car comes to a stop (the velocity goes to zero) in a short time, Δt.

 

[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?