A question from Resnik about g-force

[vela]

All this trouble can be avoided when using vectors for vector quantities from day 1 of learning physics. Even the physics-didactics community agrees with this nowadays. A good side effect is that you get used to vectors on a very intuitive level early on, and this helps to understand the more abstract level necessary for more advanced topics like electrodynamics or continuum mechanics, where it gets full vector calculus.

I think the problem isn't really about the concept of vector vs. scalar; it's about precision in mathematical notation. In my experience, most students don't really get that $\vec F$ and $F$ are two different mathematical objects and will randomly interchange them, so they'll write, for example,
$$\vec F_y = \vec T \sin\theta - mg = ma.$$

 

[vanhees71]

Sigh, yes, looks all too familiar :-(.

 

[rudransh verma]

I think the problem isn't really about the concept of vector vs. scalar; it's about precision in mathematical notation. In my experience, most students don't really get that $\vec F$ and $F$ are two different mathematical objects and will randomly interchange them, so they'll write, for example,
$$\vec F_y = \vec T \sin\theta - mg = ma.$$

Exactly. I am one of those. The thing is when you are presented with lot of right information at once then brain doesn't grasp anything at all. Its the mistakes we do makes us learn anything. Spending time working out all the things which are wrong or not possible helps very much. Removing the wrong fog in the brain helps us to clearly see the truth.
Solving problems is a great way to do it not just merely reading the texts.

 

[vanhees71]

It's the only way! Just passively reading a physics book or, even worse, listening to a lecture or videos won't help to learn the material at all. You have to already read a physics book with a pencil and paper and then do the problems thinking yourself without looking at the solutions too early. In short words: get active!

 

[hutchphd]

An adjunct to this process for, shall we say, the less precise thinker (moi) is to cultivate that little inner voice that continuously asks "does that make sense?" in as many ways as is possible. This includes reflexively looking at units (dimension) and thinking about simplified limiting cases with every major calculational step. It is a very useful skill and has managed to keep me from becoming a complete lunatic worrying about signs. Purely defensive on my part but very useful for everyone.

 

[rudransh verma]

An adjunct to this process for, shall we say, the less precise thinker (moi) is to cultivate that little inner voice that continuously asks "does that make sense?" in as many ways as is possible. This includes reflexively looking at units (dimension) and thinking about simplified limiting cases with every major calculational step. It is a very useful skill and has managed to keep me from becoming a complete lunatic worrying about signs. Purely defensive on my part but very useful for everyone.

Well I do that to a extent I get off topic. I hope you are not trying to say me a lunatic. It takes time to process all that and I am processing information. No way I am going blindly in one direction. But we make mistakes and I believe in one time or the other you are told of your mistake and it’s this one. I realized now I was thinking I know it but I don’t. It happens and it’s completely normal. You should understand this instead of just saying I am done with this. Maybe what is easy and completely irrelevant to you is not actually it.

 

[vela]

Exactly. I am one of those.

My hope is that you not only understand the difference between $F$ and $\vec F$ now but that you take away the more general lesson that the notation matters. Whereas before this thread, you may have thought $p=mv$ and $\vec p = m\vec v$ were the same equation, you'll now know they mean different things.

 

[vela]

Its the mistakes we do makes us learn anything. Spending time working out all the things which are wrong or not possible helps very much. Removing the wrong fog in the brain helps us to clearly see the truth. Solving problems is a great way to do it not just merely reading the texts.

Some expressed frustration earlier in the thread, but I wanted to say I think it's good that you even thought to ask your questions. You can't learn from your mistakes if you don't even realize you're making them.

 

[rudransh verma]

Some expressed frustration earlier in the thread, but I wanted to say I think it's good that you even thought to ask your questions. You can't learn from your mistakes if you don't even realize you're making them.

Ya! I come here with high hopes because I feel I can get my answers here from you guys.

 

[hutchphd]

I certainly intended no offense to you. I was pointing out that the best answer to your question may not be the one you seem to be demanding. For me, such attention to detail would often preclude getting to a useful result. And it would indeed drive me crazy.
It was a suggestion learned from a lifetime. Sometimes the forest cannot be seen because of the trees, and you just keep going without really undrstanding. Eventually, if you take care, it works out.