Recent content by Forrest T

Anyone?

@JeffKoch I understand what you're saying, but... In The Feynman Lectures on Physics, Volume I, an exploration of torque produces a motivation for the definition of the vector (cross) product. I think there is a similar procedure with work, but I don't know why work is defined as a scalar...

Yes, please humor me. lol.

I am assuming that I don't know anything about energy, if that is possible.

I did not want to go off of what I wrote in my first post because I wanted to understand the motivation for the definition of the dot product. Is it possible to answer my question without presuming that I know anything about energy? Why is energy a scalar anyway?

The point of that equation is that the addition of work follows the rules of scalar addition rather than vector addition. For example, \vec{F} \neq F_{x} + F_{y} + F_{z} but W = W_{x} + W_{y} + W_{z}

I guess I am trying to justify the definition rather than derive it.

I am trying to derive the equation for work in three dimensions. Here is what I have so far: In one dimension: \int ^{b}_{a} F_{x}dx = \int ^{b}_{a} m\frac{v_{x}}{dt}dx = \int ^{b}_{a} m\frac{v_{x}}{dt}v_{x}dt = \int ^{b}_{a} mv_{x}dv_{x} = \frac{1}{2}mv^{2}_{b} - \frac{1}{2}mv^{2}_{a}...

Here's a better way to phrase my question: How can you show that \sum W = W_{x} + W_{y} + W_{z} using the work-energy theorem in one dimension \int^{b}_{a} F_{x}dx = \frac{1}{2}mv^{2}_{b} - \frac{1}{2}mv^{2}_{a} and basically anything other than the three-dimensional definition of work?

How do you know that?

Why doesn't it have a direction?

I am trying to understand why work is a scalar, without knowing ahead of time that work is defined as: W_{ab} = \int ^{\vec{r_{b}}}_{\vec{r_{a}}} \vec{F} \cdot d{\vec{r}} Essentially, I am trying to understand how this definition was derived (based on the one-dimensional work-energy theorem...

hey everyone! i have flipped through quite a few textbooks on physics, chemistry and calculus, searching for one that presents motivates its derivations of equations and discussions of the concepts involved. primary sources (or those accounts of a theory written by its discoverer) which...

I looked for syllabi online before starting this thread, but I didn't find what I was looking for (with the exception of MIT). I think I'll try the book by Atkins. Thanks for your help!

Would someone please recommend an introductory textbook on general chemistry? I would like a well-motivated text that makes use of calculus, preferably one written for honors level general chemistry courses (such as the one at the University of Chicago). Thanks for your help!