- #1
- 14,429
- 7,872
A common student misconception is that when a ball is thrown straight up in the air, at the point of maximum height, where the velocity is zero, the acceleration is also zero. This can easily be dispelled by observing that, if indeed the acceleration were zero when the velocity is zero, the velocity would not change and the ball would remain at maximum height forever. We all know this does not happen and that under the constant acceleration of gravity, what goes up must come down.
All this is good, but I wonder to what extent the issue is befuddled when students encounter the example of a block that, when given an initial kick, slides on a horizontal table until it comes to rest. In this case we teach that the net force is kinetic friction and equal to μkmg. Therefore, the acceleration that opposes the velocity is also constant and equal to μkg. At this point the proverbial astute student might ask, why does the ball in the previous example return back to where it came from whereas the block in this example does not? After all, they are both moving under a constant acceleration that initially opposes the velocity, are they not?
Yes, but ... the expert understands that the constancy of frictional acceleration is only an approximation and that the force known as friction is phenomenologically velocity-dependent and goes to zero as the velocity goes to zero. In other words, the acceleration of the block is constant until it is not. Is this confusing to the novice or what?
When I teach kinetic friction, I address this apparent paradox by juxtaposing the ball and block examples and explaining that the constancy of the block's acceleration is only an approximation, valid for a range of velocities until the block is just about ready to come to a stop. At low speeds, there is "stick and slip" behavior with progressively more "sticking" until there is no more "slipping."
It's not bad practice to pretend that the acceleration due to friction is constant. It is good practice, however, to clarify that an object achieving zero velocity under the influence of a net conservative force has reached a turning point while an object achieving zero velocity under the influence of a net non-conservative force comes to rest and remains at rest. Perhaps this is a more intuitive way to illustrate the difference between conservative and non-conservative forces to students whose exposure to the definition of work is mostly recent.
All this is good, but I wonder to what extent the issue is befuddled when students encounter the example of a block that, when given an initial kick, slides on a horizontal table until it comes to rest. In this case we teach that the net force is kinetic friction and equal to μkmg. Therefore, the acceleration that opposes the velocity is also constant and equal to μkg. At this point the proverbial astute student might ask, why does the ball in the previous example return back to where it came from whereas the block in this example does not? After all, they are both moving under a constant acceleration that initially opposes the velocity, are they not?
Yes, but ... the expert understands that the constancy of frictional acceleration is only an approximation and that the force known as friction is phenomenologically velocity-dependent and goes to zero as the velocity goes to zero. In other words, the acceleration of the block is constant until it is not. Is this confusing to the novice or what?
When I teach kinetic friction, I address this apparent paradox by juxtaposing the ball and block examples and explaining that the constancy of the block's acceleration is only an approximation, valid for a range of velocities until the block is just about ready to come to a stop. At low speeds, there is "stick and slip" behavior with progressively more "sticking" until there is no more "slipping."
It's not bad practice to pretend that the acceleration due to friction is constant. It is good practice, however, to clarify that an object achieving zero velocity under the influence of a net conservative force has reached a turning point while an object achieving zero velocity under the influence of a net non-conservative force comes to rest and remains at rest. Perhaps this is a more intuitive way to illustrate the difference between conservative and non-conservative forces to students whose exposure to the definition of work is mostly recent.