The laws of motion are all one needs to solve a wide range of problems.
Unfortunately, there are alternate viewpoints that work some of the time
but which in the end are inconsistent with the laws we have described.
The purpose of this page is to point out some popular ways of getting
confused, or even getting the wrong answer.
Using the wrong name, or using the wrong concept
To begin with, we have to know what name goes with what concept, and
understand the concepts themselves. Acceleration is different from velocity,
and velocity is not quite the same thing as speed. "Energy," "power,"
"pressure," "momentum," and "velocity" are not alternate names for force.
Students will sometimes use one word when another is appropriate, either
because they are misnaming a concept or because they are applying
the wrong concept.
Mass and weight are distinct, too. This distinction is very hard to maintain, because
all weights have mass, and because
there is no word like "weigh" that means "determine the mass of this object."
If you reread the instructions we gave for the simulation of the Towed
Truck you will see that the same object could be used both as
a mass (on the truck) or as a weight (on the hanger), and that we were forced to refer to
"weights" that were being used as masses.
Using yourself as the coordinate system
Riding around in a car gives us a lot of experience with velocity and
acceleration. The car even has an accelerator! So this could be a
good source of relevant experience. Unfortunately, there is an aspect of
riding in a car that confuses more than it informs: it becomes very easy to
adopt a point of view that the car is standing still and the world is rushing
by. When you are moving in a straight line at constant speed, this is
unobjectionable; indeed, as you sit reading this you are moving east at about
1000 miles per hour (due to the rotation of the earth), and in another direction at 65,000 miles per
hour as the earth orbits the sun, and still faster than that due to the
rotation of the galaxy -- and not only are you unaware of these motions, there is no
measurement you can do that would detect them.
However, a problem arises when the velocity of the car changes,
for example, by going around a curve. Most people believe there is a
force pulling them towards the outside of the curve. All they actually
experience is that the seatbelt, car seat, or car door exerts a force
towards the inside of the curve, and they invent the outward force to
explain it. They are regarding themselves as not moving in the car, and
so there must be an outward force that the inward forces are balancing
(an application of the Law of Inertia).
But this is not the right point of view.
As a car goes around a
curve, it is accelerating towards the inside of the curve. If the passengers
obeyed the Law of Inertia, they would continue in a straight line and end up
in the bushes on the outside of the curve.
This is not the consequence of some force pulling out, but rather the lack of a
force pulling in.
Fortunately, the car seat, the seat belt, and
the car door exert forces on the passengers towards the center of the curve
to prevent this. The magnitude and the direction of the net force on the
passengers is given by the Law of Force and Acceleration.
We can avoid introducing unnecessary forces if we don't use a corrdinate system
that is being carrying around by the object that is being studied.
Discuss the car from the point of view of someone standing on the sidewalk.
The acceleration force
Some people try to turn acceleration into a force, using the Law of Force and Acceleration, and include this "acceleration force" in the set of forces that are
acting.
For this to work at all, the "acceleration force" has to be in the opposite
direction as the acceleration.
The diagram at right shows how this point of view would discuss a falling ball.
Gravity acts downward, and there is an upward force (labeled "reaction") that
"balances" gravity; its magnitude is given by mass x acceleration.
One objection to the introduction of the "reaction" force is that it doesn't
obey the Law of Interaction: if this is the force acceleration imposes on the
object, there is no force that the object "imposes on acceleration."
In the theory of motion we are trying to teach, the "reaction" force
doesn't exist. Instead, there is an unbalanced force (gravity) acting on the
ball, and this causes the downward acceleration.
In general, the Net Force is the combination of all the forces that are
acting on the object, and doesn't appear separately; it is the net force that causes the
acceleration of the object.
The force of the hand
Consider a ball that has been thrown upward. Some people try to discuss
this situation as a competition between the downward force of gravity
and an upward "force of the hand."
There are three possible interpretations. Sometimes, the discussion
really is about how the ball was thrown. But in fact, it doesn't matter
how the ball achieved its upward motion; the issue is what happens next.
But we believe that more commonly what people mean by "the force of the hand" is either the velocity
itself, or a closely related concept called momentum (this is the mass
multiplied by the velocity). These are not forces, and calling them a force is confusing, but
the issue may only be one of communication. If we change the words to
say that the ball starts with an upward velocity (or momentum) and that
the force causes this to change, we are back to the Law of Force and
Acceleration
Net Force = mass x (rate of change of velocity)
= rate of change of (mass x velocity)
= rate of change of momentum
Just please don't call the velocity (or the momentum) a force.
Another version of the same communication problem comes
in describing the car that fails to stay on a curving road.
Some people will say, "the force of the velocity pushed it
off the road." This gets the physics professors all upset,
because
falling off the road doesn't need at force at all.
A force would be needed to keep the car going around the curve.
But the statements "The velocity caused the car to go off the
road" or "The momentum carried the car off of the road"
are fine.
Using the Law of Interaction
Here's a common kind of physics question.
The car has suddenly stopped, and there is a backward force
of the seat belt on the passenger. The question is, how big is
this force?
Some people will try to use the Law of Interaction here,
and conclude that it is the same size as the force of the
passenger on the seat belt. This is perfectly true, but not
useful. There wouldn't be a force on the seatbelt if there
wasn't a passenger; the passenger is causing the force, and to
determine the size of the force we have to consider the passenger.
Once we have found out how large is the force of the seatbelt on
the passenger, we can discuss
how large is the force of the passenger on the seatbelt
(the manufacturer of the seatbelt might want to know this,
but the passenger doesn't care).
Some people try to turn acceleration into a force, using the Law of Force and Acceleration, and include this "acceleration force" in the set of forces that are
acting.
For this to work at all, the "acceleration force" has to be in the opposite
direction as the acceleration.
The diagram at right shows how this point of view would discuss a falling ball.
Gravity acts downward, and there is an upward force (labeled "reaction") that
"balances" gravity; its magnitude is given by mass x acceleration.
One objection to the introduction of the "reaction" force is that it doesn't
obey the Law of Interaction: if this is the force acceleration imposes on the
object, there is no force that the object "imposes on acceleration."
