Navigating Through Physics Problem-Solving Challenges

[americanforest]

I recently changed my major to Physics (from Computer Engineering) and love the subject. However, there is a problem. Even after doing tons of problems at home to study, there are questions on test that I just can't wrap my head around. The way I try to solve problems is to set them up without any numbers, only with variables, v for velocity etc and find a general equations. However, I often find myself in algebraic conundrums which take forever to solve (ie Quadratic formula). I'm actually quite good at math. I understand all the concepts like the back of my hand. I have friends who can do these problems without studying nearly as much as me. Am I just not cut out for Physics? What can I do to help my problem solving skills? It's very discouraging, having changed my major to something which inspires me and which I love, only to find that I may not be capable of doing it. Please help.

 

[teknodude]

Solving problems is good, but don't forget to learn the theory/fundamental concepts behind the problem. Anyone can do the algebra and punch #'s into the calculator.

 

[cristo]

Anyone can do the algebra...

Can they? Many people take algebra for granted, whereas there is quite a lot of skill to manipulating an equation correctly, which only comes naturally after a lot of practice. And, if you manage to manipulate an equation correctly, then I'd say you were using theory and fundamental concepts!

 

[leright]

I recently changed my major to Physics (from Computer Engineering) and love the subject. However, there is a problem. Even after doing tons of problems at home to study, there are questions on test that I just can't wrap my head around. The way I try to solve problems is to set them up without any numbers, only with variables, v for velocity etc and find a general equations. However, I often find myself in algebraic conundrums which take forever to solve (ie Quadratic formula). I'm actually quite good at math. I understand all the concepts like the back of my hand. I have friends who can do these problems without studying nearly as much as me. Am I just not cut out for Physics? What can I do to help my problem solving skills? It's very discouraging, having changed my major to something which inspires me and which I love, only to find that I may not be capable of doing it. Please help.

I'm sure you're capable. Maybe your math is just a little weak, but that will improve with time and practice. Everybody has their strengths and weaknesses. However, usually solving quadratics is not too big of a deal...it sounds like your math is just a bit weak and you need some practice.

 

[CPL.Luke]

yeah, you may want to pick up a book of algebra roblems to practice manipulating equations.

You're really ahead of the game though if your trying to solve the equation in variables first, most people don't do that until far later in their physics careers.

 

[FrogPad]

I recently changed my major to Physics (from Computer Engineering) and love the subject. However, there is a problem. Even after doing tons of problems at home to study, there are questions on test that I just can't wrap my head around. The way I try to solve problems is to set them up without any numbers, only with variables, v for velocity etc and find a general equations. However, I often find myself in algebraic conundrums which take forever to solve (ie Quadratic formula). I'm actually quite good at math. I understand all the concepts like the back of my hand. I have friends who can do these problems without studying nearly as much as me. Am I just not cut out for Physics? What can I do to help my problem solving skills? It's very discouraging, having changed my major to something which inspires me and which I love, only to find that I may not be capable of doing it. Please help.

When I took my first university physics course we were allowed to use cheat sheets. I had to write down EVERYTHING. Let me give you an example.

In an ideal capacitor you can write the capacitance as:
$$C = \epsilon \frac{S}{d}$$

Now if I had a question that asked for the distance between two plates of a capacitor with a capacitance of C and a surface area of S, what is the distance". I wouldn't be able to 'see' $C = \epsilon \frac{S}{d}$ and just write $d = \epsilon \frac{S}{C}$. Instead I would have to look at my 'cheat-sheet' and find the expression $d = \epsilon \frac{S}{C}$.

Or, let's say we had something like:

$$\frac{1}{\frac{a}{b}}$$ it would take me a awhile to simplify it as $\frac{b}{a}$.

All of this just comes down to algebra. Once I had practice all of those hand waiving magic tricks made sense to me. Things used to feel like they just magically appeared out of thin air.

Just practice! If you like physics a lot, then just go through as many physics problems as you can, but keep an algebra book next to you.

Also, realize that there are times to solve symbolically and times not too. For example, the current through a NMOS can be expressed as:

$$i_D = \frac{1}{2} \mu_n C_{ox} \left( \frac{W}{L} \right)_n (v_{GS}-V_t)^2(1 +\lambda v_{DS})$$

Now let's say you are given values for $\mu_n, \,\,\, C_{ox}, \,\,\, W_n, \,\,\, L_n, \,\,\, V_t, \,\,\, \lamda, \,\,\, v_{DS}$

If you are asked to find $v_{GS}$ you could yes solve this symbolically, but you would save some time if you did some multiplication and got a decimal equivalent. So pick and choose your times...

 

[americanforest]

When I took my first university physics course we were allowed to use cheat sheets. I had to write down EVERYTHING. Let me give you an example.

In an ideal capacitor you can write the capacitance as:
$$C = \epsilon \frac{S}{d}$$

Now if I had a question that asked for the distance between two plates of a capacitor with a capacitance of C and a surface area of S, what is the distance". I wouldn't be able to 'see' $C = \epsilon \frac{S}{d}$ and just write $d = \epsilon \frac{S}{C}$. Instead I would have to look at my 'cheat-sheet' and find the expression $d = \epsilon \frac{S}{C}$.

Or, let's say we had something like:

$$\frac{1}{\frac{a}{b}}$$ it would take me a awhile to simplify it as $\frac{b}{a}$.

All of this just comes down to algebra. Once I had practice all of those hand waiving magic tricks made sense to me. Things used to feel like they just magically appeared out of thin air.

Just practice! If you like physics a lot, then just go through as many physics problems as you can, but keep an algebra book next to you.

Also, realize that there are times to solve symbolically and times not too. For example, the current through a nmos can be expressed as:

$$i_D = \frac{1}{2} \mu_n C_{ox} \left( \frac{W}{L} \right)_n (v_{GS}-V_t)^2(1 +\lambda v_{DS})$$

Now let's say you are given values for $\mu_n, \,\,\, C_{ox}, \,\,\, W_n, \,\,\, L_n, \,\,\, V_t, \,\,\, \lamda, \,\,\, v_{DS}$

If you are asked to find $v_{GS}$ you could yes solve this symbolically, but you would save some time if you did some multiplication and got a decimal equivalent. So pick and choose your times...

That's a lot of the same problems I have. Good to know I'm not alone. I guess it just seems ridiculous to have to study algebra when I'm taking Differential Equations and Multiple variable Calculus. Thanks for the advice guys!

 

[mathwonk]

all professors of calculus know that the biggest obstacle for most students is basic high school algebra.

one reason is the foolish emphasis on AP calc in HS instead of teaching algebra well.

another is over use of calculators.

 

[FrogPad]

That's a lot of the same problems I have. Good to know I'm not alone. I guess it just seems ridiculous to have to study algebra when I'm taking Differential Equations and Multiple variable Calculus. Thanks for the advice guys!

Yup. Did the same thing man. I actually got a C in calc I, II, and III . Then every math class after that I've had an A. My foundation (algebra) was horrible. It's better now, definitely not great. I just needed practice, and it sucks that the calc series had to be my algebra practice. Just hang in there... it will get better, but do yourself a favor and practice over winter and summer break. It will make your life easier.

 

[FrogPad]

another is over use of calculators.

that's what killed me.

HS taught me how to not think when doing math.

 

[mathwonk]

i am grading calculus now and the problem that my students are having the hardets time with is fiunding the arc length of (3/4)x^4/3 - (3/8)x^(2/3).

basically because they cannot do the algebra to show that

[x^(1/3) - (1/4)x^(-1/3)]^2 + 1 = [x^(1/3) + (1/4)x^(-1/3)]^2i explained over and over that (a-b)^2 + 4ab = (a+b)^2, so that if ab = 1/4, as it does in all these problems, then (a-b)^2 + 1 = (a+b)^2 is a perfect square. no use. more than half of a stronger than average class cannot get it. this is basic junior high algebra.

 

[teknodude]

Wait... Is it the math that's discouraging you or physics? Maybe i read your post wrong, but i got to get back to cramming.

Also i didn;t learn the basics of algebra until after i graduated HS. Gotta love that k12 education. Guess not everyone can do the algebra

 

[americanforest]

Now I think it's definitely the math part that discourages me. I can set up all the physics equations and can see how it should be solved theoretically. I think I lack the skill or manipulating equations as well as I would like. I just never thought it could be my math, since I do well in relatively advanced math classes, but I think you guys have a point about the importance of and how many people neglect algebra.