Does acceleration affect impact energy vs constant velocity?

[sophiecentaur]

That can happen momentarily in an elastic collision.

Yes; as with a bouncy spring but does this relate to a car collision? Only in Bugs Bunny lol.
The scenario is a bit undefined but, then, the whole problem is a bit vague. Without some disciplined Physics we can’t conclude anything.

 

[Dale]

Yes; as with a bouncy spring but does this relate to a car collision? Only in Bugs Bunny lol.
The scenario is a bit undefined but, then, the whole problem is a bit vague. Without some disciplined Physics we can’t conclude anything.

I don’t think the question is specific to car collisions. It seems to me that the OP just wants the simplest basic principles to use to reason. So simplifications like elastic collisions and Hooke’s law are specifically requested.

 

[sophiecentaur]

I don’t think the question is specific to car collisions. It seems to me that the OP just wants the simplest basic principles to use to reason. So simplifications like elastic collisions and Hooke’s law are specifically requested.

Except he is using car driving as a scenario. Are we discussing a lab experiment with an object hitting a spring / buffer? No, I don’t think so. The OP seems to want to do the whole thing in one go and doesn’t seem to accept that the full scenario is very complicated. If the scenario involves an instantaneous collision then it doesn’t matter whether the object is accelerating or not. Hooke’s law cannot come into it in zero time. If the impact takes time and displacement then more details are needed.
The only collisions discussed in elementary Physics are with idealised billiard balls etc. and possibly with coefficient of restitution less than unity. That’s a single impact with a given approach velocity. Those problems are simple and soluble. Introducing car crashes is miles further along the learning path.
I think the requests for Hooke’s law etc are basically requests for ways to approach the problem. The formulae are just tools and advice is needed how and when to apply them. So we have to start with a sensible problem.

 

[Dale]

Except he is using car driving as a scenario.

I don’t think that car collisions are central to their question. They mentioned it once after many posts either not specifically about cars or even about things that were explicitly not cars.

 

[sophiecentaur]

I don’t think that car collisions are central to their question. They mentioned it once after many posts either not specifically about cars or even about things that were explicitly not cars.

The OP could clear up the context of the question.

It all depends on where the original question arose in his mind. If it came from a list of text book - type questions then It was not helpful for any student because it's totally open ended and has no answer. The wording of the question suggests that it comes from a real life situation (PF regularly gets that sort of question). Bringing in the car scenario suggests that the car is appropriate - the wording of the post implies an attempt to use Physics - speak to re-state a practical question. A question, posed in that way needs to be unpicked to produce an answerable one. High school physics cannot deal with many real life situations; there are too many variables involved in real life and we (PF) can be helpful by pointing our the parts of a question that are actually answerable and the parts that are for 'later'.

 

[Herman Trivilino]

So, acceleration can increase the energy at the moment of impact vs constant velocity

It's not the acceleration itself that increases the energy. It's the force, and only if that force continues to act after the collision.

In my opinion you don't need to worry about that because the statement of the problem doesn't specify that detail.

I think all that's needed is an understanding that the energy is given by $\frac{1}{2}mv^2$, an expression that doesn't include the acceleration.

 

[sophiecentaur]

It's not the acceleration itself that increases the energy. It's the force, and only if that force continues to act after the collision

Exactly. If the Force is enough to keep the object accelerating after / during contact (especially at the same rate) then it would need to increase to keep up with the extra work. Newton 2 tells you that. So, to deal with the acceleration factor, you would need to know the masses of the object and the target (you can't just assume the Earth as the target because there will still be distortion. In addition, if you really want to solve the problem, you need to know about the deformation(s) and the modulus - in fact, the whole dinner menu.

The point I have already made is that the requirement for constant velocity or acceleration is the major sticking point. The OP wanted help with appropriate Formulae. Unfortunately, for a complete solution, you have to be using the appropriate formulae at each stage and to have the actual `Physics in mind' before launching into calculations.

There are a thousand and one scenarios that can be discussed without all that aggro and the answers set you a long way on the road to understanding this stuff. Inventing a random problem can be pretty difficult if you don't know enough to start with. This is why we learn things using tried and tested problems - very demanding for someone who wants a quick answer, unfortunately.

If this stuff were easy, they insurance companies and Forensic police would often find it easy to decide whose fault 'it' was. Instead they have to use masses of past evidence - tables etc. to decide the sort of thing the OP was asking for.

 

[sophiecentaur]

I think all that's needed is an understanding that the energy is given by 12mv2, an expression that doesn't include the acceleration.

Very often that's a very good approximation but what about when the collision is when the brakes have just been applied hard? (Tyre marks often tell a useful story; zero length if the driver had died at the wheel.)

 

[Herman Trivilino]

Very often that's a very good approximation but what about when the collision is when the brakes have just been applied hard?

Not relevant. The speed of impact is what's given in this simple problem. Why make it harder on the OP?

 

[sophiecentaur]

Not relevant. The speed of impact is what's given in this simple problem. Why make it harder on the OP?

The OP starts off with reference to constant velocity and constant acceleration. How can he be convinced that those ideas cannot be explored at this level. How to convince him without making very clear that simple mechanics can’t do it? Read the first post again and you may see what I’m getting at.

 

[PeroK]

This is a good example of the principle of conservation of thread momentum, requiring no ongoing impulse from the OP.

 

[sophiecentaur]

conservation of thread momentum,

Possibly momentum in the wrong direction - the best sort for New Year

 

[Herman Trivilino]

The OP starts off with reference to constant velocity and constant acceleration. How can he be convinced that those ideas cannot be explored at this level. How to convince him without making very clear that simple mechanics can’t do it? Read the first post again and you may see what I’m getting at.

I think all that's needed is an understanding that the energy is given by $\frac{1}{2}mv^2$, an expression that doesn't include the acceleration.

 

[sophiecentaur]

Why make it harder on the OP?

You made this comment earlier. You used the formula for KE which, of course, is correct but your implied reasoning is almost totally maths based and your conclusion is totally maths based. Shutters often come down for many PF visitors.

I have a bit of a crusade to present help in as tangible way as possible. If you are in a Pub, trying to explain your thoughts on a topic you will often be without pencil and paper but you can usually do it at a suitable level without.

Einstein's opinion was that many things can be introduced in the form of pictures and mental models. Imo people need to be helped into a state where formulae have meaning for them. It's always possible to ramp up the difficulty as a thread develops but the 'PF momentum syndrome' often takes a thread further and further into the higher realms and a poor OP shuffles off from a potentially very good thread because it's too hard.

 

[Herman Trivilino]

Einstein's opinion was that many things can be introduced in the form of pictures and mental models.

He also said that things should be made as simple as possible, but no simpler.

I take your point about discussions and images and mental models. Those things are an important part of an education. And there are plenty of opportunities to introduce them. I just don't think this is one of them. I believe the authors of the question were probing to see if the student understands that the speed, not the acceleration, matters in this context.

Expert problem solvers love to layer on complexities. Which is entirely understandable because it's fun and instinctual. It's a big part of what made us experts to be begin with, but it can often confuse the novice problem solver when too much complexity is introduced too quickly or in an inappropriate context.

 

[sophiecentaur]

in an inappropriate context.

The 'context' is in the title; namely that varying speed and acceleration are relevant in a simple collision that is treated as being instantaneous. So I really think that my nagging is appropriate. The problem has to either be really basic or very complicated. The can of worms from a 'real' situation needs much more detail than the OP was acknowledging. High School Physics doesn't go that far.

 

[Dale]

High School Physics doesn't go that far.

I think my post 24 gets them as far as they need for the simplest example that doesn’t “simplify away” the thing they are interested in. It is as simple as possible, but not simpler.