How to get better at theoretical homework problems

[astroman707]

I’m having lots of trouble in my honors physics class with the theoretical homework problems that are assigned. The entire concept of learning to solve things theoretically, and then applying it is brand new to me. I’m decent at figuring out the applied problems, but pure theory stumps me. I know that doing more regular application problems will increase my understanding, but I was wondering if anyone had any tips or tricks they used when solving theoretically.
Here’s a typical example of a theoretical problem on my homework, which is what most of my homework problems are:
—Two small balls are suspendes side by side from two strings of length L so that they touch in their equilibrium position. Their masses are m and 2m, respectively. If the left ball(of mass m) is pulled aside and released from a height H, it will swing down and collide with the right ball(of mass 2m) at the lowest point. Assume the collision is elastic.
• How high did each ball swing after collision?
• Both balls again swing down, and they collide once more at the lowest point. How high will each swing after this second collision?

 

[jedishrfu]

You have to first make a drawing of what the problem is describing and then from there determine what intermediate values you need.

As an example, consider a pool shot you plan to make where the cue ball hits one ball and that ball bounces off a cushion to strike another ball which goes into a pocket. First you’d draw a picture, then determine what intermediate values you can compute from cue ball hitting the first ball and do it again for that ball hitting the last ball.

Of course, you could work it backward too determine the allowed trajectories to drop the last ball in the pocket and then where on the intermiediate ball the cue ball needs to hit and then where on the cue ball you need to strike to make it all happen.

These problems are in fact a sequence of small events each of which you can apply your knowledge of physics too to answer the problem.

A simpler, example is the ball rolling off a table where you break it into two parts. One part determines how long before the ball hits the floor if dropped from the same height. Given the time, you can then determine how far the ball moves horizontally and putting things together determine its trajectory and final impact point.

 

[Delta2]

When you are faced with theoretical problems, you got to decide how to "attack" the problem. And by doing so you got to decide what your "main weapons" going to be in attacking the problem. Your weapons for attacking problems are going to be some of the axioms, theorems and laws and principles you learn during the theory learning.
For the example you give, it is obvious it has to do with collisions, so from theory you know that the main laws governing elastic collision is conservation of momentum and conservation of energy. Those two laws are going to be your two main weapons for attacking this problem. Also the problem has to do with movement inside the gravitational field of earth, so conservation of energy or maybe the work-energy theorem is a weapon for this problem too. Those laws and theorems are going to be your primary weapons and together with the secondary weapons of theorems in algebra and calculus are the whole weaponry you will need in order to successfully attack the problem.

Of course you might say that your problem lies on how you apply the laws , axioms and theorems from theory to the specific cases of the various problems. You just have to solve many problems and see how the laws are applied again and again in order to get over this and to get familiar with how the laws are applied.