Writing up the physics problems (Physics 205-206)

Writing up the physics problems (Physics 205-206)

Model solutions. Your book has hundreds of examples – these are carefully constructed to be clear and readable. Let them serve as a model for how you should write up a problem. Below – the italicized material + figure(s) should be included in your problem writeup.

Sample problem. Consider the following problem (just for illustration):

A hot air balloon has just lifted off and is rising at the constant rate of 2.0 m/s. Suddenly one of the passengers realizes she has left her camera on the ground. A friend picks it up and tosses it straight upward with an initial speed of 10.0 m/s. If the passenger is 2.5 m above her friend when the camera is tossed, how high is she when the camera reaches her?

State the problem – if you’re in a hurry, photocopy it and paste it at the top of your final solution.

Rough Draft the problem. Normally you should rough draft your problems and when you “get it” do the final solution.

Explain in words what you are doing. When you write up solutions to problems, be sure to explain your reasoning. Don't just give us the final numerical answer or the end formula. We already know what it is! Instead, we want you to overcome the roadblocks that get in your way as you progress through the problem. An appendix in the text by Tipler gives the answers to odd-numbered problems. These are only skeleton answers; we want full solutions (like the "sample problems" of the text). You need to explain what you are doing in words. The explanation does not need to be long or detailed, but it must exist if you are to earn full credit. For example, in the above problem

This is a one dimensional problem (up and down; along the vertical; along the y axis) and there are two positions of interest: the passenger and the camera; we will treat each of these as POINTS.

Map out the logic. (thinking aloud – on paper): I’m going to treat the motion of the passenger as constant velocity; the camera is in accelerated motion due to the gravitational force. I may try two separate equations where time is a shared parameter.

Diagrams and definitions. In almost all cases, the first step in solving a problem is to draw a diagram showing the geometry of the situation. The diagram will organize your work and point out ways to proceed.

The diagram is often a good place to define variables that you will need as well. Using the sample problem as an example again, a diagram and variables y1, y2 would be reasonable for the positions and v1 and v2 for the velocities of the passenger and camera, respectively.

Diagram of problem.

Do full problem for full credit. All of the relevant equations need to be there, put down logically. Do not plug in numbers before getting final equations (see below). Reasonable but not GROSS jumps in algebra that someone can follow are allowed as long as it can be understood (particularly by you 3 months later). For the above problem:

From Diagram:

Motion of Camera: y2 = v2 t – ½g t²;

Motion of passenger y1 = yzero + v1 t.

When position of camera and passenger are the same, the camera has reached her, at t = tfinal:

i.e., y1 = y2, which implies v2 tfinal – ½g tfinal² = yzero + v1 tfinal.

Solving for tfinal: tfinal = -(v1-v2) /(g/2) ± [Sqrt{(v1-v2)² -4 yzero g/2}]/2(g/2) (most important part!!).

INTERPRETATION: ± sign – gives TWO tfinals: one corresponds to on the way up, the longer time corresponds to on the way down. The shortest time is on the way up.

Numerical substitution: Substituting in the values for v1, v2, yzero, and g we find that tfinal (on the way up) = 0.42 seconds.

tfinal = 0.42s

Any additional comments or insights: If v2 is not large enough or yzero is too large, the camera will not reach the passenger (for example, if the argument of the square root becomes negative, you end up with an imaginary number for tfinal! – not an allowed solution.)

Do partial problem for partial credit. If you can't solve a problem completely, then hand in a start. If you have a plan for solving the problem but can't execute it, then write up the plan and submit. You will even get some points for saying nothing more than "This problem combines constant velocity motion + free fall with an initial velocity”.

If you can't solve the problem then at least do something: sketch the situation and define a few relevant variables. State a relevant principle. If you come up with a silly result (e.g. a negative kinetic energy), then tell us that it's silly and you've earned a point (or two). If you run out of time, then write a sentence about how you would solve the problem if you did have time. Writing down your thoughts can clarify them and lead you to your goal. If nothing else, they might earn you points.

BE NEAT AS POSSIBLE: Your solutions do not need to be obsessively neat, but they do need to be legible. Be as neat (and complete) as possible.

Not Torture: The problems in a physics course are not meant as tools of torture – they are meant to teach you how to reason, put your thinking into equations, and interpret your results.

SO HERE IS THE ENTIRE PROBLEM:

This is a one dimensional problem (up and down; along the vertical; along the y axis) and there are two positions of interest: the passenger and the camera; we will treat each of these as POINTS.

I’m going to treat the motion of the passenger as constant velocity; the camera is in accelerated motion due to the gravitational force. I may try two separate equations where time is a shared parameter.

From Diagram:

Motion of Camera: y2 = v2 t – ½g t²;

Motion of passenger y1 = yzero + v1 t.

When position of camera and passenger are the same, the camera has reached her, at t = tfinal:

i.e., y1 = y2, which implies v2 tfinal – ½g tfinal² = yzero + v1 tfinal.

Solving for tfinal: tfinal = -(v1-v2) /(g/2) ± [Sqrt{(v1-v2)² -4 yzero g/2}]/2(g/2).

Note the ± sign – gives TWO tfinals: one corresponds to on the way up, the longer time corresponds to on the way down. The shortest time is on the way up.

Substituting in the values for v1, v2, yzero, and g we find that tfinal (on the way up) = 0.42 seconds.

tfinal = 0.42s

Comment: If v2 is not large enough or yzero is too large, the camera will not reach the passenger (for example, if the argument of the square root becomes negative, you end up with an imaginary number for tfinal! – not an allowed solution.)