Maybe I shouldn't have started this blog now, not with everything that's been going on.

Exam in my mechanics class today. But before that I should say that some of the students (four actually) arranged a review at my cousin's house yesterday.

For this I had to cut short my Holy Week vacation.

I took some problems from the book I used in college, whose pages were so brittle that they ripped when the fan blew through them. It was a source of our amusement for some time.

This was before one of the students showed up with our textbook though. From that textbook, I found out there was a problem where a block started out on top of a frictionless ramp, hits another block at the bottom, and both go on to slide horizontally across a frictional surface.

The first part uses conservation of energy. The second part is of course a collision and conservation of momentum. The third part uses the principle of friction.

I let the students spend a better part of half an hour trying to make heads or tails out of that one before I just gave them the solution, which only covered less than twenty lines. A couple of the students already got how to solve it, but for the others, I still had to clarify it for them, especially how the final velocity of the first part becomes the initial velocity involved in the second part and so on. But ultimately I did not include that in the exam.

There were some problems on friction, particularly one that had the pulling force at an angle from the horizontal (and the direction of motion). Since this required having summation of forces along the x- and y-axes that is not what they are used to, it was of sufficient difficulty for me to include it in the test, with slight modifications to the numeric values, of course.

I also included a problem on energy that I made up. It was a trick question, changing the mass of the ball going down the ramp and the incline of the ramp, and asking for the change in velocity, which is nil. But that was already 15 points in the bank for them if they got it right (The questions were 5 points each). For red herring purposes I also asked for the length of the ramp when the angle of inclination is changed, although it is not used for computing the velocity.

Unfortunately, in hindsight it wasn't clearly stated in the problem that the vertical height does not change, so there were some who did not get the shortcut.

Luckily (and to ward off questions) I wrote in the instructions that no questions would be entertained, and that if there was a part of the problem that was unclear, they should state their assumptions.

I also included another friction problem that was a direct application of their experiment in the lab, of tilting a plank and recording the angle when the block on the plank slides down. Hopefully that was easy for some of them.

Lastly, for momentum and collision, I had two problems: one for one-dimension, another for two-dimensions.

These were both derivation problems, not getting a numeric value from application in one equation, but two, of which they had to substitute again to get one of the three unknown values left (the second one cancelled itself out).

One looked for the mass of the struck object given the mass of one object, and the ratio of its velocities before and after the collision. The other asked for just the angle given the initial and final velocities of one object.

These we also discussed in the review. No charity cases for these guys, or so it seems. I'll elaborate tomorrow.