Midyear Exams

Results for many were not bad at all. However, most of you continue to make the same fundamental errors. I believe this goes to the very root of what is wrong with the way most of you learn. You are still looking for the simplest combination of numbers to get an answer without understanding the physical relationships behind the equations.

For example, faced with a cart going down a hill most of you stick what is PE initial in an equation which requires delta PE. You may actually write Delta PE in your equation, but you use just PE initial. This is because delta PE requires two numbers and so is too hard for your brain.

When you come down a hill delta PE = mg (h at bottom - h at top). I would hope that high school juniors in AP or honors classes would know that h at the bottom - h at the top is a NEGATIVE number. In other words, I would hope that you would know which way is up! and therefore which way is down.

Another very common error involves acceleration in rotational motion. When at the top of a curve, one can assume that you got there by going up and are leaving by going down. This means that your velocity is changing from up to down which means your acceleration is down or negative. Another instance where you demonstrate whether or not you know which way is up! However, adding a negative sign is apparently an extremely laborious process which you are not willing to undertake.

Many of you are showing a complete disregard for what conservation of momentum means by writing m1v1=m2v2. This is almost never true. If total momentum is zero in a system with two objects in it then m1v1= - m2v2 before and after any collisions or other interactions between the two. However, this is not true if the total momentum is not zero. You should start with the full blown m1v1+m2v2= m1v1'+m2v2'.

Many of you still writing Funknown = Mg even when there is acceleration and you should use Funknown =Fnet -(Fknown) [Fknown is -Mg in many vertical cases]. Also Funknown = Fnet is WRONG when there are other forces acting such as gravity. In other words, you frequently use incorrect equations just because they have one term on the right side instead of the two terms the correct equations have.

Finally, for now anyway, is the fact that you incorporate Mg in equations concerning horizontal motion. This is wrong, usually for two reasons. One, Mg is a vertical force and does not cause horizontal acceleration. Two, in those cases where an object is traveling horizontally, there are other vertical forces canceling gravity, such as a normal force, or some combination of normal and tension forces.