I started my presentation on inclined planes the way I've always started it -- with a quantitative demonstration. I placed my venerable rechargeable 310-g PASCO fan cart, whose fan produces a force of 0.26 N, on a PASCO track. To what angle should I incline the track so that the cart remains on the track in equilibrium?
I demonstrate the solution using the standard three-step Newton's Law problem solving procedure -- draw a free body, break the weight into components, and write Fnet = ma in both directions. In this case, because acceleration is zero, the weight component down the incline mg sin θ equals the 0.26 N force of the fan. Solving for θ gives an angle of about 5 degrees. That's easy (and impressive) to verify with an angle indicator.
The next problem I pose posits the same cart released from the top of a 10 degree incline; what will be the cart's acceleration? This time, instead of solving myself in front of the class, I have each student work through the problem himself. When someone gets an answer, I hand him one of the fan carts, a motion detector, and a labquest -- it's his job to verify the answer. Usually we predict an acceleration of 0.87 m/s/s, and we measure something in the neighborhood of 0.77 to 0.86 m/s/s. I'm happy with that -- at most 11% off from the prediction.
However: Yesterday a group kept getting between 0.56 and 0.60 m/s/s for the acceleration of the cart. Now, rather than 11% off, this group was 31%-35% off. That didn't seem right. What was going on?
The first words everyone spewed were "because of friction." Stop it. It's rare that the true cause of a laboratory discrepancy can be attributed solely to neglecting or miscalculating friction. And in that rare case that friction is indeed the issue, "because of friction" is never an appropriate answer. Explain how the force of friction, or the work done by friction, would change the relevant equation; and then convince me that the measurement is different from the prediction in a way that would be accounted for by that force of or work done by friction.
This group measured an acceleration that was smaller than predicted; but the other groups were pretty much right on. That implied that the carts might have been different in some way.
These PASCO fan carts operate on a rechargeable battery. "Could our cart's battery be dying?" the group asked. Let's see... the weight component down the incline of mgsinθ = 0.54 N is independent of the fan. It's the force of the fan up the incline that would change depending on the battery, and that fan force is subtracted from 0.54 N to calculate the net force. A smaller fan force due to a dying battery would mean that the net force down the plane would be greater, not smaller, giving more than the predicted acceleration.
So the cart's battery wasn't dying. We realized that two of my three carts were newly purchased over the summer. I used a force probe to measure the force of the fan on the new carts -- I got 0.32 N, more than the 0.26 N from the old fan. Aha!
What a wonderful AP Physics 1 problem you've discovered. You could describe the situation... then ask some of the questions below:
* How would you experimentally measure the cart's acceleration after it's released from the top of the 10 degree incline?
* Predict the cart's acceleration after it's released from the top of the 10 degree incline.
* How would the cart's acceleration change if rather than being released from rest it were instead given a brief shove to cause it to move up the 10 degree incline?
* The cart's acceleration is measured to be substantially less than the prediction. Does that mean that the force of the fan was greater or less than the assumed 0.26 N?
* How could you experimentally measure the force provided by the fan?
I know when I write any sort of physics problem -- whether for the College Board, for my book, or for my class -- I often begin with an actual situation I've encountered in my laboratory. Do you have an experiment that lends itself to a good AP Physics 1-style verbal response sort of question? Post it in the comments, or email me; maybe I'll use that as the basis for a "Mail Time!" post.