# Homework Help: Formula Mania: Please Give

1. Feb 15, 2004

### holly

Buddy, can you spare a formula?

Physics Expert Marcus has suggested first-year physics students get a list of formulas, memorize when they are used, and learn them.

That is EXACTLY what I started to do earlier today! My list is very lean, however.

Can anyone help us beginning students amass some formulas and hints on when to use them? I have gone thru the boards and looked for formulas, but honestly, I can't make heads nor tails out of them, especially those using calculus.

So far, I have (from Marcus et al) d=1/2gt^2 and one about when something is raised, it uses Joules, and is mgh where g is 10m/s^2. And I have F=ma, which someone else on the boards says uses N-s, and then a=F/m, which I guess will always have the time unit squared. But I have a=delta v/t interval of change, and which one is the best? And I've got p=mv (for momentum). I need work ones, power ones, impulse, KE, so forth. They are proliferating like a bunch of little bunnie rabbits.

Thank you for any help. Perhaps if the weaker students such as myself get a good list of formulas, we will stop posting easy stuff and leave the boards clear for more intriguing problems! I solemnly promise to go away for at least a month.

2. Feb 15, 2004

### marcus

they passed out funny hats at the Christmas party. I get to wear the Fireman's hat. There was a vote of the membership. You get to mention this once and thats it.

You have already earned an A+ in physical science this semester by your brilliant adaptation of a Famous Saying of Newton's. We do not want people who ask physics questions to go away. We like questions. Making a list of formulas is only part of it. Once you get the basic formulas down you will still have questions. You may be surprised by this but it has been widely observed that even after learning the
first semester's list of formulas there are still things about nature which one cannot understand.

easy does it
you are making good progress
rome was not built in a day
when is the midterm and/or final?

3. Feb 15, 2004

### HallsofIvy

What Marcus is saying, in his own inimitable way, is that memorizing formulas is a really, really bad way to learn physics. Physics is not formulas. Physics is ideas and concepts. Learn those instead.

4. Feb 15, 2004

### chroot

Staff Emeritus
I'm trying to decide if I should post my own personal list.

- Warren

5. Feb 15, 2004

### marcus

Please do Warren, I cannot imagine a better outcome from this thread.

especially if you still have your list from freshman year

6. Feb 16, 2004

### chroot

Staff Emeritus
These are the formulas I put on flashcards to help me study the GRE, in no particular order. I feel they are formulas that all physics students should understand and have quick at hand.

ONE-DIMENSIONAL KINEMATICS:

$$\begin{equation*} \begin{split} \textrm{acceleration} &\equiv a(t) = a\\ \textrm{velocity} &\equiv v(t) = v_0 + at\\ \textrm{position} &\equiv x(t) = x_0 + v_0 t + \frac{1}{2} a t^2 \end{split} \end{equation*}$$

SIMPLE HARMONIC MOTION:

$$\begin{equation*} \begin{split} \textrm{frequency} &\equiv \omega = \sqrt{k / m}\\ \textrm{velocity} &\equiv \omega x_{max} \sin (\omega t + \phi)\\ \textrm{acceleration} &\equiv \omega^2 x_{max} \cos (\omega t + \phi) \end{split} \end{equation*}$$

PERIOD OF A PHYSICAL PENDULUM:

$$T = 2 \pi \sqrt{\frac{I_{support}}{M g L_{cm}}}$$

CHANGE IN ENTROPY:

$$\Delta S = \int_i^f \frac{dQ}{T}$$

BERNOULLI'S EQUATION:

$$p_1 + \frac{1}{2} \rho v_1^2 + \rho g y_1 = p_2 + \frac{1}{2} \rho v_2^2 + \rho g y_2$$

$$\varepsilon = -N \frac{d}{dt} \phi_B = -N \frac{d}{dt} (\vec B \cdot \vec A)$$

$$\nabla \times \vec E = -\frac{\partial}{\partial t} \phi_B$$

$$\oint_F \vec E \cdot d\vec s = -\frac{\partial}{\partial t} \phi_B$$

BINOMIAL EXPANSION:

$$(1 + x)^n \approx 1 + nx$$

CONSERVATION OF MOMENTUM:

general case:

$$v_{1f} = \frac{m_1 - m_2}{m_1 + m_2} v_{1i} + \frac{2 m_2}{m_1+m_2} v_{2i}$$

$$v_{2f} = \frac{2 m_1}{m_1 + m_2} v_{1i} + \frac{m_2 - m_1}{m_1+m_2} v_{2i}$$

stationary target:

$$v_{1f} = \frac{m_1 - m_2}{m_1 + m_2} v_{1i}$$

$$v_{2f} = \frac{2 m_1}{m_1 + m_2} v_{1i}$$

E FIELD DUE TO A POINT CHARGE:

$$\vec E = \frac{q}{4 \pi \epsilon_0 r^2} \vec e_r$$

E POTENTIAL DUE TO A POINT CHARGE:

$$\phi = \frac{q}{4 \pi \epsilon_0 r}$$

E FIELD DUE TO A DIPOLE:

along dipole axis:

$$E = \frac{1}{2 \pi \epsilon_0} \frac{qd}{z^3}$$

E POTENTIAL DUE TO A DIPOLE:

$$\phi = \frac{zqd}{4 \pi \epsilon_0 r^2}$$

LORENTZ FORCE LAW:

$$\vec F = q (\vec E + \vec v \times \vec B )$$

ENERGY OF A PHOTON:

$$E = hf = \frac{hc}{\lambda}$$

blue photon with $\lambda$ = 400 nm has energy E = 3.1 eV.

red photon with $\lambda$ = 700 nm has energy E = 1.77 eV.

CENTRIPETAL ACCELERATION:

$$a = \frac{v^2}{r}$$

CENTRIPETAL FORCE:

$$F = ma = \frac{m v^2}{r}$$

STOKES' THEOREM:

$$\oint_\Gamma \vec C \cdot d \vec s = \int_S (\nabla \times \vec C) \cdot \vec n dA$$

GAUSS' THEOREM:

$$\int_S \vec C \cdot \vec n dA = \int_V \nabla \cdot \vec C dV$$

GAUSS' LAW:

$$\oint_S \vec E \cdot \vec n dA = \frac{Q_{int}}{\epsilon_0}$$

$$\nabla \cdot \vec E = \frac{\rho}{\epsilon_0}$$

SNELL'S LAW:

$$n_1 \sin \theta_1 = n_2 \sin \theta_2$$

TOTAL INTERNAL REFLECTION:

$$\theta_c = \sin^{-1} \left( \frac{n_2}{n_1} \right)$$

DIFFRACTION MINIMA:

$$a \sin \theta = m \lambda$$

$$r_s = \frac{2 G M}{c^2}$$

$$v = \frac{a + b}{1 + \frac{ab}{c^2}}$$

PARALLEL-AXIS THEOREM:

$$I_f = I_i + Mh^2$$

WORK DONE IN A CONSTANT-PRESSURE PROCESS:

$$W = p \Delta V$$

WORK DONE IN AN ISOTHERMAL PROCESS:

$$W = n R T \ln \frac{V_f}{V_i}$$

WORK DONE IN A CONSTANT-VOLUME PROCESS:

$$W = 0$$

DOPPLER SHIFT APPROXIMATION:

$$u \cong \frac{\Delta \lambda}{\lambda} c$$

VELOCITY OF WAVE PROPAGATION IN A MEDIUM:

taut string:

$$v = \sqrt{\frac{\tau}{\mu}}$$

sound waves:

$$v = \sqrt{\frac{B}{\rho}}$$

- Warren

7. Feb 16, 2004

### paul11273

Holly,
While memorizing formulas is not necessarily a bad thing, it can hurt you if that is what you will rely on to get through.
It is better to concentrate on learning concepts, and that will help you to learn when to apply the formulas you have committed to memory.

This is what I do...
As we cover material in class, I have one sheet (now it is about 3 pages) where I write important formulas and a quick note about it.

I use this sheet as a quick reference sheet to jog my memory while doing practice problems.

Here is another tip...by "practice problems" I do not mean assigned HW. I mean going way beyond the HW and doing a ton of extra problems. By doing this extra drilling, memorization is automatic because you have worked with the formulas so much. I try to do this for every chapter as we cover it. When midterm comes around, I have quite a lot of problems worked out. Then I go back and try to redo them. This helps to solidify them in my memory, and is kind of a confidence builder. The last thing I want one week from a major exam is to get bogged down on some crazy problem, wasting time and killing my momentum.

One last thing. I read in your impulse question that your professor has a less than desirable attitude, and the text you are using kind of lacks. I have found that purchasing the solution manual for a text (if there is one) helps me greatly. It lets me practice problems, and I know that if I get stuck, the solution manual will usually unstick me. This forum has been great too!

As for asking everyone for our formula lists, it would probably be better if maybe once a week you post what topics you have covered, and we can send you some focused notes / formulas which cover that material. Just an idea...

8. Feb 16, 2004

### himanshu121

I agree with Halls

So u have got list for most of the formulas(thnxs Chroot). u should remeber those formulas +++++with Concepts as well

9. Feb 16, 2004

### marcus

tuning the discussion to Holly's particular situation

Paul's advice is good and Warren posted a great list for Geek Freshmen and maybe even sophomores too.
Holly is being given a glimpse of the Culture.

But we really have to tune this to a two-year college in a dry oily part of texas
and to the non-engineers introductory physical science course
where the math is highschool algebra---in part already forgotten

we need a list which is not (like Warren's) for techie majors at Stanford but which is fine tuned for a different setting

It is a difference not in kind but in degree. Holly is as smart as anyone here, and Nature is the same for everybody, but she has only highschool algebra at best and probably mistrusts that.

so this is like building a bridge across the gulf of mexico. its a big jump.

maybe Holly the truth is that EVERYBODY HAS TO MAKE THEIR OWN LIST
you have to sit in class and figure out by listening to the prof what formulas you have to memorize
it should be be the right list for you and for the class
(Warren's list was the right one for him in the class he took)

Personally I think the one you came up with already was very good.
so maybe we got off on the wrong track when we started giving you suggestions.

Let's post again what you have so far:

10. Feb 16, 2004

### marcus

So far, I have

d=(1/2)gt2
(for when something is falling and you know, or you want to find out, the time it takes)

PE = mgh
(when something is raised, it uses Joules)

F=ma

and then a=F/m
(acceleration always has the time unit squared)

a=delta v/delta t
(acceleration is the change in speed divided by the time interval)

p=mv
(for momentum, how it's defined).

I need work ones, power ones, impulse, KE, so forth.

They are proliferating like a bunch of little bunnie rabbits.

------------------------
my comment is
this is the same kind of thing as Warren's list, the difference is only in difficulty and amount

now we all know what you have to do with such a list
you have to practice and practice so you get to really understand
when and how to use the formulas
(that is, like HallsofIvy suggests, the concepts embodied in them, like the potential energy something has because it is up, become second nature)

the concepts embodied in the formulas must become "operational" in your head---which only happens by working examples---which is why they hand out long homework assignments which appear, and in fact are, rather repetitious. and if the prof does not assign enough then you do them on your own, while you are eating a peanut butter sandwich or going to sleep at night, and if the textbook does not have enough examples then you find another textbook. and so it goes.

i suspect this process is already occurring to some extent with holly which is quite fascinating, given the different cultural setting.
if so, good for you and for us.

11. Feb 16, 2004

### marcus

I need work ones, power ones, impulse, KE, so forth.

Well, write down the KE formula
we are all waiting in suspense

12. Feb 16, 2004

### holly

W O W

Geez, I leave for a few hours and when I come back, horrible calculus-y formulas are all over the place. Sin, sin, everywhere a sin...help! Thank you chroot, but you must have mistaken me for someone with a brain...thank you ALL for the help, thank you singly and grouply for the ideas...for the idea of understanding the concept, etc...for cleaning up my little list of formulas so far...

The professor DOESN'T supply ANY formulas whatsoever. Nope. He says if we understand intuitively, we can discern the formula. Well, let's dig up Galileo and tell him he should have discerned F=ma & saved himself a bunch of trouble. Even big ol' brains can't just intuitively build formulas! I MUST memorize them! I MUST do that though it isn't the optimal thing! And I HAVE bought other texts, I have bought study guides, I have been scouting around for formulas...

So, I will do as suggested and just slog thru problem by problem, and ask youse for help, and write down whatever formulas you use.

And I thank each of you from the bottom of my heart! And the rest of my class will thank youse too when I share the formulas. And somebody in west Texas thinks youse are great.

13. Feb 16, 2004

### marcus

holly,
the prof does not supply any formulas whatever
and says if you understand intuitively you will be able
to discern the formula!

this is not a standard course in college physics
it is not something I am familiar with
I am afraid of giving you advice that does not
fit the actual situation on the ground.

this must be a new approach to teaching physics
maybe someone here has encountered this kind of course
and can give you more appropriate coaching

I want to hold off giving advice because I dont have a good
feel for what's going on. But I am still very curious.

If you wouldnt mind, would you please tell us some
homework problems or some exercises from out of the textbook.
this would give me, and whoever else is interested, some idea
of what its like to be learning "intuitive physics"
or "low-formula physics"
if that is what we are dealing with here

I am trying, just out of imagination, to think of what a problem could be in that book:

"Two stones are dropped out of a tall building---from one from one story above streetlevel and the other from nine stories above streetlevel.

which stone hits first and how much longer does it take to fall?

A. 9 times longer to fall
B. 5 times longer to fall
C. 3 times longer
D. they take the same length of time to reach the ground

(imagine the stones are streamlined enough so air resistance plays no role)

14. Feb 16, 2004

### chroot

Staff Emeritus
I believe good physics is about equal parts quick-recall and derivation.

In other words, you need a handful of quick relationships at your disposal. You know, little gems like <E> = 3/2 kT. Sure, you can derive that from stat. mech., but that would take far too long.

On the other hand, you need to be able to mold your memorized equations to the task at hand, which often requires some manipulation, approximation, or other "editing." Knowing when and how to make those edits determines the difference between a formula-dependent physics student and a truly creative one.

Also, don't forget dimensional analysis -- it's an often-overlooked, but very powerful tool.

- Warren

15. Feb 16, 2004

### holly

Actually, that sort of "dropping stones" scenario is what the teacher talks about! We have heavy and thin skydivers falling, too, and we have melting ice blocks, sliding crates, and steel balls rolling down inclines onto carpeting. I can follow that sort of thing...yes, I agree it can be "intuitive," but the problem comes when the *conceptual* part is emphasized, but the *math* part is tested! Because, how else can you test what the person knows? But it seems silly to me to SAY the course has no math, but have it actually be FULL of math...just today, we were listening to a lecture about a big coal cart and a little coal cart having a collision, and the big one was going faster and one way, and the little one was slower and the other way...and the upshot was, "Okay, dorky non-science majors, what might happen? Might the big one slow down and keep going the same direction?" Duh, yes...but then, wham-o, on the test, we have to figure out the momentum of each, and the velocity once they collide...we can't just say, "Gosh, da big one won but it slowed down!" That's why I am desperate for formulae.

Okay, I am stuck on this problem, it's part of our book's companion volume, Practical Physical Science: We have "Bronco," one of our little characters, pushing a block of ice up an incline. The ice weighs 500 N. The incline is 6m long, it is 3m high at the high end. We ignore friction..."How much force is needed to push it up the incline?" How the heck can I figure that out? I look at my little list of formulas, I try to make the ones with an "F" in them work...but I don't know...Then, we must answer this: "How much work is required to push it up the incline?" Well, I don't know. W = F d, I have that written down, but...I didn't know how to get the F in the first part of the problem...Two pages later, there is a little drawing of a guy with an overbite who is intoning, "Making the distinction between momentum and kinetic engery is high-level physics." And we have a pig-tailed girl saying, "Let equations guide your thinking!" Only, as they say around here, "No hay." It means, There ain't any equations lying around for me to use...

Thank you.

16. Feb 16, 2004

### chroot

Staff Emeritus
Hmmm holly, it sounds like professor is really doing a rather poor job if he tests you with methods you've never seen used in class.

- Warren

17. Feb 16, 2004

### marcus

holly, the situation is strange and unfamiliar with lots of
contradictions---this is not the beginning college physics class we are used to.

if you lifted it straight up 3 meters you would do
1500 joules of work.

you gonna have to do the same amount of work to push it up the
incline
no free lunch, same 1500 joules either way, just more gradual than heaving it straight up

so what force, if applied for 6 meters, does 1500 joules of work
has to be 250 newtons of force

half the force, and push it twice as far----same work as twice the force push it half as far

250 x 6 is same as 500 x 3

with Bronco and the guy with the overbite and the peppy girl with pigtails it sounds more and more like the end of civilization as we know it

18. Feb 16, 2004

### NateTG

Another option is to make a list of all of the forces that are acting on the block, and make the total equal to zero.

19. Feb 16, 2004

### marcus

are the exams going to be "short answer"
like choose between answers A, B, C, and D

or are they written out

20. Feb 16, 2004

### holly

*sigh*

Well, I am thinking I ought to start placing my questions over in the K-12 board, tho' it IS a college course, because it is too easy for youse and is messing up the boards? Our poor little college here, they try...but...it's only 25 years old...we don't even get to use the lab for the lab that comes with the course, we are told to do the labs at home, I spent all weekend trying to find a 2-meter long piece of aluminum guttering and a 1/2 steel ball & a meterstick.

Thank you for the help in the block of ice problem, I guess there wasn't an equation for it, just thinking. Either way, I'm doomed.

Thanks again...

BTW, the exams, they are a mix, they have the multiple choice, they have short answer, and they have finishing diagrams, the only test so far, it was 74 questions in 50 minutes, I didn't finish...

Last edited: Feb 16, 2004
21. Feb 16, 2004

### NateTG

Re: *sigh*

No, this stuff is typical of a freshman physics course.
The ice block question can be solved using energy, or using a free-body-diagram. (Energy is probably easier, but you may not have covered it.)

22. Feb 16, 2004

### marcus

the distinction between K-12 help and college help
is artificial
you are fine where you are and fine if you move over there
(Nate is right it does sound like college freshman subject matter tho)

sounds like metric units are part of the problem
(for many of you it is the first encounter with them and there are the frustrating details like not having a meter-stick or
a kilogram scale)

what did they want you to do with the ball rolling down the
gutter?

23. Feb 16, 2004

### holly

The steel ball had to be rolled down the gutter at 30, 60, 90, & 120 cm up from the bottom of the ramp. We were supposed to measure how high the ball was. And note how far it rolled. And roll it three times each cm division. Then, we were supposed to prop up the ramp more, and this time roll it three times from how high the ball was initially, ignoring the 30, 60, etc divisions. Then prop it up more, etc. Then average how far it rolled, then answer what conclusions we drew from our data. And make a graph, too. I didn't know what to conclude. It didn't go as far when the ramp was steeper. Oh, and answer why we didn't bother with K.E. calculations but just P.E. ones, and it said "only physics types know why these intermediate steps can be skipped, and why high-level thinking uses energy to solve these problems" or some such drivel. At least the lab didn't feature Nellie Newton or Bronco this time!

24. Feb 16, 2004

### Pesci

hello,
My name is David and I'm new to the site and to physics.
i just returned to college after a minor set back and I have choosen
the wounderful world of physics as my "main course". since returning to school i am basically starting out with a foundation less than that of a highschool student. i am currently taking a general physics course to get me started and i have found a great site that has quite a few basic formulas. the address is http://www.hazelwood.k12.mo.us/~grichert/sciweb/formulas.htm [Broken]

hope it has a at least a little of what you are looking for.

[?]

Last edited by a moderator: May 1, 2017
25. Feb 17, 2004

### holly

Thank you very much, I will go over to that site right now! Because my homework is just busting my chops.