Kinematic equations ##\textbf{purely}## from graphs

[nasu]

Could this work?

View attachment 337042

How do you get the formula $s=\frac{(v_0+v_f)t}{2}$? From the graph or "from algebra"?
Actually, what is the purpose of the graph here?

 

[Lnewqban]

Actually, what is the purpose of the graph here?

The graph goes together with a question to the OP.
Please, see quote of post 29.
It seems that your answer to that question is no.

 

[brotherbobby]

Wow! And whose intuition would that be? Take a class of twenty students and you could find twenty different intuitions at the start of the process. Or would it be a voting procedure?

Not true. All students intuitively believe, for example, that an object takes longer to rise than to fall. Though it's false. Likewise, physics learning is riddled with misconceptions that have been found to be cross cultural.

 

[Orodruin]

All students

I’d be very careful making such sweeping statements. In all my years studying and teaching physics, I have never encountered this.

That said, intuition is something that comes from experience. Advanced physics does not and cannot generally be taught based on intuition as students generally will have no experience with the subject or situations. This can only be built by working with the subject.

To teach students that physics is intuition based seems like a big mistake in my book. It just leads to students attempting to apply their classical intuition to relativity and quantum mechanics.

Edit: Physics is built on empirical evidence. If this matches student intuition - great, but experiment is where the focus shoukd be.

 

[brotherbobby]

I’d be very careful making such sweeping statements. In all my years studying and teaching physics, I have never encountered this.

Ask yourself.
Every time you throw a ball up, don't you feel that it takes longer to rise than to fall?
Not only all students. But all humans feel that. It's one area where nature fools our senses. Physics tells us that it is not so.
All generalisations are not false. I will leave it to you to find the logical error in the statement if they were.

 

[Orodruin]

Every time you throw a ball up, don't you feel that it takes longer to rise than to fall?

No.

But all humans feel that.

Wrong. Simply wrong.

 

[brotherbobby]

No.Wrong. Simply wrong.

You were born with exceptional skills.

I did my studies in misconceptions in physics which I would urge you to look into someday. These misconceptions have been verified across cultures and have found to be robust, i.e. resistant to instruction.

We humans are way more similar than we are different. Unless we are prodigies.

 

[Hill]

misconceptions

I've never had this misconception, never knew anybody who expressed this misconception, and, for a little test, asked a minute ago my wife, who never studied physics, what does her intuition say about it. She said, "The same."

 

[boneh3ad]

You were born with exceptional skills.

I did my studies in misconceptions in physics which I would urge you to look into someday. These misconceptions have been verified across cultures and have found to be robust, i.e. resistant to instruction.

We humans are way more similar than we are different. Unless we are prodigies.

The problem is you are painting with an incredibly broad brush. Intuition comes from lived experience, not the aether. Some may be more common than others but nothing is universal.

This thread is wild.

 

[nasu]

The graph goes together with a question to the OP.
Please, see quote of post 29.
It seems that your answer to that question is no.

I mean, what is the point of showing the graph? You obtain the desired equation by combining the definition of average acceleration $a=\frac{v-v_0}{t}$ with the formula $s=\frac{v_0+v_f}{2}$. None of these are derived from the graph and the last one is something assumed without proof. The fact that the expression #as# happens to be equal to the area under that graph is of no consequence to the derivation.

 

[brotherbobby]

The problem is you are painting with an incredibly broad brush. Intuition comes from lived experience, not the aether. Some may be more common than others but nothing is universal.

This thread is wild.

When it comes to objects pushed it pulled, falling and rising, sounds, lights, heat... we humans have the same experiences. We all believe heavy objects fall faster than lighter objects intuitively, don't we?

 

[Orodruin]

You were born with exceptional skills.

I did my studies in misconceptions in physics which I would urge you to look into someday. These misconceptions have been verified across cultures and have found to be robust, i.e. resistant to instruction.

We humans are way more similar than we are different. Unless we are prodigies.

It is one thing to claim that most people have a particular trait. It is another to claim that all do. Please do provide a study showing that everyone suffers from this particular misconception.

As was also already mentioned, intuition is not something you are born with. It is something that is developed by experience and exposure.

 

[Orodruin]

We all believe heavy objects fall faster than lighter objects intuitively, don't we?

First of all, no. We don’t all believe that. The case for when we do believe that is in the case with air resistance - where it typically is not a misconception. Very few of us have actual experience with things falling in a vacuum and therefore no intuition about it.

 

[boneh3ad]

When it comes to objects pushed it pulled, falling and rising, sounds, lights, heat... we humans have the same experiences. We all believe heavy objects fall faster than lighter objects intuitively, don't we?

I'll repeat my position: some misconceptions are more common than others; nothing is universal (well, except death and taxes).

And, to be fair, it's probably really difficult for those of us choosing to post on a physics message board to remember exactly what our intuition told us in our teenage years. But I can definitively say my intuition tells me none of the things you have suggested currently even though you have suggested several times (#35, #37) that we all likely still believe them because this intuition is somehow baked into all humans.

As an aside, I cannot stand the overreliance on graphs for teaching kinematics. It almost inevitably leads to high school students associating velocity with the slope of the $x$-$t$ curve and then the uniform interpretation of derivatives and slopes of something rather than as rates of change more generally. The end result is they often have a fairly myopic view of what derivatives and integrals are and the connection with other physical problems.

 

[brotherbobby]

First of all, no. We don’t all believe that. The case for when we do believe that is in the case with air resistance - where it typically is not a misconception. Very few of us have actual experience with things falling in a vacuum and therefore no intuition about it.

You are quite wrong there.
It is a misconception in the case of air resistance too. And more so.
When a body is thrown vertically up, due to resistance acting down, it takes less time to reach maximum height than when it falls, when resistance acts up. Though our senses are tricked into thinking presicely the opposite - that it takes more time to rise than it takes to fall.

 

[brotherbobby]

I'll repeat my position: some misconceptions are more common than others; nothing is universal

The age-old misconception - "heavy objects fall faster than lighter objects" - isn't that universal?

 

[Orodruin]

You are quite wrong there.
It is a misconception in the case of air resistance too

Please show me the feather that falls at the same rate as a bowling ball in air.

So no, it is not generally a misconception.

When a body is thrown vertically up, due to resistance acting down, it takes less time to reach maximum height than when it falls, when resistance acts up.

Now you are chamging the goal posts. This is not what you were talking about in the previous post. I. The previous post you talked about objects falling, not objects going up and down.

We all believe heavy objects fall faster than lighter objects intuitively

Please stop being disingenuous.

And yiu still have nif backed up your claim that everyone (literally everyone) suffers the misconceptions you are claiming.

The age-old misconception - "heavy objects fall faster than lighter objects" - isn't that universal?

No. Please see above.

The very common misconception is extrapolating it to vacuum.

Even if everyone thought about it like that at some point (which I am not sure is even true), intuition is something that is built on experience and familiarity. Where do you draw the line on how much experience a person may obtain before testing them? Anyone who dropped two fairly heavy - but unequal - objects (such that air resistance is negligible) and actually looked at the result will know the correct result. Is that not allowed? Are the test subjects allowed to go to elementary school? High scool? University?

 

[brotherbobby]

Please stop being disingenuous.

Please don't respond to me if that is what you think am doing.

 

[PeterDonis]

I did my studies in misconceptions in physics which I would urge you to look into someday. These misconceptions have been verified across cultures and have found to be robust, i.e. resistant to instruction.

Are these "studies" published in peer-reviewed papers?

If not, they are personal theory and are off limits for discussion here.

And in any case, this thread is in the subforum for classical mechanics, not psychology. Your claims seem as dubious to me as they do to other posters, but they're off topic here even if they are correct.

 

[PeterDonis]

Thread closed for moderation.