From: Ronald Wong (ronwong@inreach.com)
Date: Tue Nov 04 2003 - 00:34:10 PST
Message-Id: <l03102805bbca0fecd2e6@[209.209.18.69]> Date: Tue, 4 Nov 2003 00:34:10 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: Re: forces/friction
Recently Jennie said:
>...i'd love some help.
>...if i am driving a car at a constant velocity, and the engine
> is exerting a force of 100N, then the force of friction balances
> that out with 100N the other way.
Right.
> now, let's say, i suddenly stop the car mid-motion and turn
> off the engine. the car will slow down and eventually
> stop because of the force of friction, which is counteracting
> the car's "desire" to keep moving because of its inertia, right?.
Right.
> But how do we describe the forces on the car during its slow-down?
> My student asked me if the only force on the car were friction
> in the opposite direction, why the car wouldn't move backwards.
That was a good question on the part of the student. It brought out the
fact that the student didn't understand the nature of friction.
My approach to physics teaching was to determine what the students knew
about a topic BEFORE I introduced it to them. In this way they could
integrate what they already knew about nature with the things that they
were about to learn. The material seemed to stick with them a lot longer
than if I simply introduced them to the topics of kinematics, dynamics,
etc. as they are so often found in physics textbooks.
I would frequently do this by means of a simple demonstration or two.
For instance: I would place a book on a table and ask the students, "What
forces are acting on the book as it lies on the table?". Some would say
none because it wasn't moving and I'd give them an initial nod of approval
because, in one sense, they were absolutely right (a point we return to
later in the presentation). Inevitably, someone would mention the force of
gravity (if not, I'd do a second demonstration that quickly got their grey
cells going - I'd drop something on the floor).
Now that they had a force acting down on the object, the next question was:
"Why doesn't it fall down?". They quickly drew the conclusion that the
table was pushing up on the book (i.e. "Holding it up"). This lead to a
series of activities where the students pushed one of their fingers down on
their desks and noticed the effect that this had on the tip of their
finger. They then pushed the finger of one hand against that of the other.
This was followed by other activities which, with time and patience,
revealed to them the properties of Newton's 3rd Law.
When we took these observations and applied them to the book sitting on the
table, the students suddenly realized that it sat there NOT because there
was no forces acting on the book but because the forces acting on the book
were balanced (Newton's 1st law had already been covered earlier through a
process similar to the one they were presently engaged in so this served as
a review in one sense). The nice part is that I didn't have to tell them
that and all I had to do thereafter was to remind them about these
discoveries whenever they forgot.
The next question, of course, was, "How do we set this book in motion along
the table?". Everybody knew that one. If they didn't give me a direction
for the "unbalanced" force, I would initially push down on the book. After
a little moaning and groaning on their part, they would tell me to direct
the unbalanced force in the horizontal direction. Doing this gave me an
opportunity to show that an "unbalanced" force changed the velocity of an
object in the direction of the "unbalanced" force (i.e. accelerated the
object in the same direction as the unbalanced force) - laying down the
groundwork for the Newton's 2nd Law.
At this point we get into friction because the next question I asked was,
"What happened to the book after it left my hand?". Everybody knew the
answer to that one too - it slowed down (it decelerated).
They also knew the answer to the next question: "Why?" - FRICTION!. They
even were able to tell me which way the frictional force must have acted to
slow the book down.
So, an "unbalanced" force acting in the direction of motion accelerates an
object and later the unbalanced force of friction acting in the direction
opposite to the direction of motion slows it down and stopped it
(re-inforcing the initial ideas of Newton's 2nd Law introduced earlier).
It was clear to them that friction opposes motion.
It was opposing the motion even as I was accelerating the book with my
pushing force.
Thus there were two forces acting during the acceleration phase of the
demonstration. The unbalanced force was NOT the "unbalanced" force
mentioned in the earlier paragraphs - the pushing force - but the
difference between the pushing force and the smaller (a conclusion the
students make - not I), frictional force.
Once the book left my hand I was no longer pushing on it and only the
frictional force remained. The unbalanced force acting on the book was now
only the frictional force and, since it was opposing the motion of the
book, it caused the book's velocity to change until it was reduced to zero.
At that point the book was at rest. It was once again simply lying on the
table and we were back to square one where only the force of gravity and
the table's reaction force were acting on the book. Just as before, there
was no frictional force. All these points would be made by the students -
not I.
That's why the "..the car wouldn't move backwards". The frictional force
brought it to rest and, once it came to rest, the frictional force ceased
to exist. There was no longer any unbalanced forces acting on the car so it
just sat there.
> is there still the force of the car engine acting in the forward
> direction even when the car shuts off?
One of the questions I asked during the demonstration was "Why does the
book keep moving after I was no longer pushing it? Why didn't it just stop?"
Earlier in the course, the class had considered
Galileo's speculations involving a ball rolling
down one inclined plane and up another in which
the latter became less and less inclined. A series
of demonstrations followed that confirmed the
conclusions that they had arrived at earlier after
reflecting on Galileo's thoughts on the matter
and allowed me to put them in a frame of mind
where they could see the connection between
uniform velocity and balanced forces. At that
point I could bring up a new concept - Newton's
1st Law (the Law of Inertia).
Their answer to the question was immediate - INERTIA! There is NO force
acting in the forward direction. Only the tendency of a body to maintain
it's state of motion ("'desire' to keep moving" as you said) is responsible
for the car's continued movement in the forward direction. That's the law.
> (and even so, if the forces were balanced before, it seems the
> net force would still be in the direction of the friction force)?
When the driving force produced by the engine was balanced by the
frictional force, the net force was zero. That's why the car moved with
uniform velocity down the road - neither speeding up, or down, or changing
directions. Once you turned off the driving force, only the frictional
force was left to act on the car. Now we have a net force and, since it is
the frictional force, the net force acts in the direction of the frictional
force. Since this is opposite to the direction of motion, the car slows
down.
> is it the ground exerting a forward force on the car?
The ground exerts an upward force on the car perpendicular to the car's
motion so it can't contribute to a horizontal force in either direction. It
does play a role in determining the size of the frictional force and thus
the rate at which the car slows down.
The important thing to remember is that there is NO forward force on the
car "...when the car shuts off".
Now Aristotle would vehemently argue otherwise
- so you are in very good company when you
expressed the idea that there should be a force
in the forward direction to account for the
continued motion in that direction. In fact,
earlier in my physics course my students would
also have agreed with you. They had been shown
examples where motion could only be sustained
by the application of a force - something that
they were very familiar with. But this was
before we considered Galileo's thought
experiments, created a few of our own, and
looked at a system where very little friction
was present (an air track) - all of this part
of a prelude to Newton's 1st Law.
> i guess a similar example would be rolling a ball and letting go...
> what other force is at work as the ball is being slowed down by
> friction in the opposite direction?
None. Friction is the only force acting on the ball in the horizontal
direction. As a result, it is an unbalanced force and, because it opposes
motion and acts in a direction opposite to the direction of motion, it
slows the ball down and brings it to rest.
Speaking of "rolling a ball":
If you wanted to test your students' understanding of the fact that
friction opposes motion, have your students consider a ball rolling up an
inclined plane.
Ask them:
1. Which way is the frictional force acting on the ball as
it rolls up the inclined plane?
2. Which way is the frictional force acting on the ball as
it rolls down the inclined plane?
3. With the answers to question 1 and 2 in mind, what is
the frictional force at the moment the ball comes to
rest just before it begins to start rolling down?
For high school physics students there are many more questions that can be
asked but more than enough has been said.
Best wishes.
ron
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