Ok, real question:
What is the best way to go about attacking physics problems. Forgive me if this sounds conceited, but I'm not used to actually getting question
wrong after I've done the reading and (felt like I) grasped the relevant concepts. I've literally
never had to work this hard for a course and
still feel utterly incompetent (did well enough on the first exam relative to the class, but that's not good enough in my eyes; I care more about what I feel my own competence level to be in a given subject).
I mean, my professor is an ass who can't teach worth a lick; in fact, when I read your posts in response to that guy's physics HW questions a while back (the vector-based stuff), you were a
hell of a lot better at explaining the relevant concepts and highlighting what information someone should be extracting from the text (in word problems) than he is. For me, I'm not sure what the problem is, really, but I am
quite frustrated (despite doing comparatively well, as I said); I just don't feel like I should be having as much trouble as I am, which is less than others are having, but for me it's a lot.
When I read the textbook, I
totally understand it-- the concepts and how they relate to the physical phenomena, the equations and how they're derived etc.; even when I do those "in-chapter" review questions, I tend to get them correct, and where I don't get the answer quickly, I follow along easily when reading the solution. But when I get to the HW problems-- which seem to be an order of magnitude more difficult than the in-chapter exercises-- it's an entirely different story. I get a good portion of them correct, but I just FEEL inept, FEEL like it shouldn't be as hard as it is. In short, I feel like I'm missing something crucial in solving these problems. By way of self-examination, I've narrowed my "problem areas" down to two (note: all "i" subscripts refer to "initial" values) :
1) I have some difficulty choosing the proper equation for the task at hand. On the surface, this would seem a trivial matter, because all you have to do is list the variables you're "given" (or ones easily derived, like the x- and y-components of vectors) and then find an appropriate equation that contains the variable of interest (the one the problem is asking for) along with the given variables and then solve for the unknown (either directly or by algebraically rearranging the equation). Fine...I'm there so far.
But what if there are two or more equations that can be employed, such as when solving for time (t) if given initial velocity and after having found the final velocity at some point P. Do you use t = (v(f) - v(i))/a ? Or t = 2 DeltaX / (v(f) + v(i))? (assuming you know the displacement along the x-axis)--- does it even
matter which equation you use so long as your calculations in finding your "given" data were correct, or should you arrive at the same answer regardless? These are the things that the professor never coached us on; my mind says that any equation should do as long as the data you're inputting is correct and it only contains a single unknown variable that can be solved for; the professor did say that a problem can be solved in several ways, so that would seem to indicate that any equation is fine if it meets the above criteria. I'm not even sure if this is my specific problem, to be honest-- I just know that for some reason, I haven't developed an intuition for how to solve these problems yet. Does that just come with practice, or are there specific strategies that will aid me in getting there quicker is what I'm asking. Granted, I haven't devoted nearly as much time to the course as I would have liked (perhaps 5 hours/week, if that; I was planning on 15 per week, which it looks like I'll have to do
).
2) I have some trouble "equating equations"-- not quite sure if that's the best way to phrase it, but it's the best I can do. This manifests itself most visibly in problems involving projectile motion for two distinct "particles", like a gun firing a bullet at an object dropped from rest at some distance. If they ask for the time when the bullet will hit the falling object, is it just a matter of finding the x-component of the bullet's velocity (based on the trajectory and initial velocity), using that as v(xi), and then rearranging deltaX = v(xi)t + 1/2at^2 to be t = deltaX/v(xi) (using the initial distance from the object as deltaX), since the 1/2at^2 term is zero due to no acceleration in the x-direction? If so, allow me to continue...
If the next part asks for the height at which the bullet strikes the object, do you simply use deltaY = -1/2gt^2 (plugging in the t value obtained previously), since the v(yi)t component of the equation is zero? Obviously, you'd subtract whatever value you got from the initial height of the object to obtain the height above the ground at which the object was struck, right? This is just me thinking aloud, so forgive me if all this is correct (which it probably isn't)-- I'm just trying to see where I usually go wrong. Ok, scrap that (but I won't delete it in case I did something wrong and you can correct my thinking)-- I have a better example:
The one question I got wrong on the exam, which was worth 15 points (which is why I ended up with an 83; considering the class' 53 average, I'm safe
), was roughly something like the following:
Suppose two people (A and B) are standing atop a building; person A releases a ball from rest. Two seconds later, person B throws a ball downward at an initial speed of 45m/s . Assuming that ball B must at least reach ball A before they hit the ground, what is the minimum height of the building. Now, this is where I feel that I would have to "equate equations" somewhere (because at that point, their y-displacements have to be equal) and just plug in the different initial conditions for ball B (the initial velocity of 45m/s and the 2 second lag), but I had a
huge brain fart and just couldn't fathom where to begin or how I would go about such a thing. I figured that if I could find either t or either of the balls' velocities at the point where their y-displacements were equal, I could use that to find the height of the building (assuming that I knew the y-values were equal but did not know their explicit value-- because if I knew the y values explicitly for where they were equal, that would be the minimum height of the building, I assume). If the other problems didn't take me so goddamned long to figure out, perhaps I would have had more time for the strategy to "come to me"-- but that's my very point....these questions are taking me far too long to do, even when I eventually find the correct answer, so I feel like I'm incompetent. : /
Even now just looking at it, I'm just dumbstruck at how I can practically
hear my mind churning and grinding to a halt when confronted with such a problem (which shouldn't even be difficult, really, considering that it's not conceptually complex). Yeah, if I stared at it for a half hour or so, it'd likely come to me, but I don't have that sort of time (on exams etc.), which is why I seek your aid.
Even the more conceptually "difficult" (in quotations because I'm sure this all seems trivial to you physics geeks
) problems involving relative velocities and stuff don't usually bother me the way this thing did. Weird.
So what do you say? Is there any effective strategy to solving these questions beyond just doing problems until your eyes bleed until you develop that intuition? I mean, I'll do that if I have to, and it's not like I did badly on the exam, considering-- I've just honestly never had this experience of feeling like my brain JUST DOESN'T WORK, or at least isn't perceiving the proper method of attacking the problems quickly enough. I've really been torn up about it, considering that I don't have this issue anywhere else-- not biology, not chemistry, not even math. Very annoying-- maybe I'm just too much of a perfectionist, but this really irks me. <grrr>
And btw, I'm sure that if and when you post the answer to that problem, I'm gonna hit myself in the head for being so stoopid and not having seen it earlier.
It just feels like something doesn't "click". It was also only with great reluctance that I decided to ask for help with this. Unfortunately, I'm an extremely prideful individual, and am loathe to admit (especially in public) that I'm having difficulty-- however minor-- with something....particularly academics. Hmph.
