On the second or third day of kinematics, after we've discussed position-time and velocity-time graphs, I introduce acceleration. I start by handing out the four - yes, only four - facts about acceleration.
(1) Acceleration tells how much an object’s speed changes in one second.
This is the fundamental definition, one we'll use again and again. It leads to stating acceleration in units of m/s per second - that way, every time a student writes a numerical acceleration with units, that student is reinforcing in her or his mind the physical meaning of acceleration.
(2) When an object speeds up, its acceleration is in the direction of motion. (3) When an object slows down, its acceleration is opposite the direction of motion.
These indicate the direction of acceleration in words students can understand. Note that I don't use the words "negative" or "positive" anywhere! Directions of acceleration and velocity are stated as left, right, up, down, north, south, etc. The language used matters here. Students may never, ever say "acceleration moves left." Nor may they say "the object accelerates to the left." They must state either fact (2) or (3), and conclude with "the object's acceleration is left."
Some practice with a PASCO visual accelerometer helps here. In the linked post, I'm using this tool to work on misconceptions about the direction of force and motion; but just stick this accelerometer on a cart on an incline, and you can have all sorts of conversations about the direction of an object's acceleration.
(4) Objects in free fall gain or lose 10 m/s of speed every second
Once we understand facts (1) through (3), then (4) is just telling us about a special case in which we know the value of acceleration. That's it. Pedagogically, it's important not to treat free fall as a BIG DEAL. Just give evidence that objects in free fall do, in fact, experience 10 m/s per second acceleration, and be done with it.
Since at this point my students are well familiar with velocity-time graphs, I like to show that the slope of a velocity-time graph will be 10 m/s per second for an object in free fall. That's easier said than done. Motion detectors generally have trouble getting good data above 20 data points per second, and classrooms aren't usually more than 2-3 meters high. Even if you're dropping a full 3 m, that gives a fall time of only 0.77 s, and only about 15 data points for the detector. Don't even talk to me about getting an object large enough and flat enough to reflect detector's sound waves consistently, but heavy enough such that air resistance can be ignored.
Oh. But I found such an object. Look at the picture.
I stored a 15 pound medicine ball for a year in a cabinet. One side flattened, as you see; and it doesn't unflatten easily. Awesome.
So a student stood on a lab table holding a motion detector on the ceiling, pointed down. A second student dropped the ball from 20 cm below the detector, with the flattened side pointing up. I got the cleanest line on a velocity-time graph that I've ever gotten from a free fall experiment! I told the LabQuest to do a linear fit on just the straight segment, and voila... 10 m/s/s was the slope.
Greg, I think this may be the first post you've ever made that I don't completely agree with!
ReplyDelete"Students may never, ever say "acceleration moves left.""
Agreed.
"Nor may they say "the object accelerates to the left.""
Why not? I too have moved away from claims like "if the acceleration and the velocity have the same sign, then the object is speeding up" to new language like "if the object is moving in the same direction in which it is accelerating, the object is speeding up," but I don't see anything wrong with saying the object is accelerating to the left. Change my mind?
I've never studied this sort of language formally, so everything that follows just comes from my own experience and is completely anecdotal. Here's my argument for preferring "the object is accelerating to the left" to "the object's acceleration is left" in most contexts: the latter phrasing implies that the object HAS acceleration, like it's some sort of entity or quantity possessed by the object, and that once the object jettisons its acceleration, its speed won't be changing anymore. That just doesn't sit right with me, though I concede that I have no problem with "the object's velocity is directed to the left."
We tackle the same problem with forces when we convince students that a force is an event, and not something that an object has. It's sort of like that with this.
In writing this reply, I've got myself all turned around. I suppose I ultimately don't mind "the object's acceleration is directed to the left," but I also don't mind "the object is accelerating to the left." You'll have to convince me why the latter is bad.
Hey, Mike... I don't like using "accelerate" as a verb of any form. In common usage, that means "speed up" - when a major misconception to bust is that acceleration can indicate slowing down as well as speeding up.
DeleteAnother standard misconception is conflating the direction of motion with the direction of motion. Would a student ever say "the car accelerates to the north" when she means the car is moving south and slowing down? Probably not... when a student tells me which way a car is "accelerating" that student is most often meaning that the car is moving in the indicated direction.
Look, you and your students are not *wrong* to say "the object is accelerating to the left." That is a correct physical statement for a car moving left and speeding up, or for a car moving right and slowing down. I have just found more success busting misconceptions by banninating the use of the verb "to accelerate."
Thanks for the reply, Greg. I agree about the common use of the word "accelerate" vs the physics classroom use. I make it a point to get kids to use the word accelerate meaning both speeding up and slowing down. As a matter of fact, I banninate the word "decelerate" in any context. It's a fight every year, but one that I don't mind fighting.
DeleteI suppose it's just a matter of teacher preference how they choose to approach these language-based issues. As long as the teacher is thoughtful and consistent in their usage, I doubt one method is much better than the other. Thanks for sharing your thoughts.
Aah... once you focus on using "accelerate" as a verb to mean either slowing down or speeding up, then you've accomplished the same thing. Nice. We're fighting on different fronts of the same battle. :-)
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