Problem solving strategies

Now we come to less trivial situations involving Newton's Laws. A lot of these problems can seem darned near impossible if you don't go about solving them the right way. It takes a lot of self-discipline to logically apply Newton's laws to obtain the correct answer. Remember this is physics, not philosophy. The answers you get can be tested experimentally. There are never two right answers to well posed physics problems. So if you get stuck do not:

1. Write down something that you know is wrong and continue.
2. Decide to guess an equation.
3. Decide to guess an answer.
4. Fudge your solution because you think you know the answer right answer and it's just not working out the way you think.

Instead, realize that the answers are derivable from Newton's laws. You just need to be logical enough to see how to do it. In order to aid you, you should follow the following advice. If you don't, you have nobody but yourself to blame when you screw up.

1. Draw a diagram. If you want, draw a rough sketch to get yourself off the ground. Then identify all the forces in the problem. You saw an example of this above with the picture of the hand and the weight in fig. 1.4.
2. Draw a ``free body diagram'' for each object. That is, draw a picture of an object, and draw only those forces that act on the object. Include all the forces that act on the object.
3. Figure out a good coordinate system to use for each object. That is how the coordinate system is to be oriented. Them apply in component form. That is for the x and the y components separately. Remember to use symbols such as etc. instead of numbers like 3 kg.
4. Solve the equations. If you've done everything right, you should be able to solve for all your unknowns.
5. Check limiting cases. What happens if this mass goes to zero? This one to infinity. What if this angle becomes 90 degrees? You get the idea. If all the limiting cases seem to make sense, and the units check out, then you've probably solved the problem correctly. If they don't check out, at least now you'll have a clear logical description of your work and will be able to go over it to check for mistakes.

Now let's looks at some examples.

• Tension on an inclined plane
  • Draw a diagram
  • Draw free body diagrams
  • F=ma in component form
  • Limits
• Mass held by two ropes
  • Draw a diagram
  • Draw free body diagrams
  • F=ma in component form
  • Solve the equations
  • Limits
• pulleys