Call students’ attention to any stationary
object in the room in common view, such as a book on a table. Then
ask students to consider what the stationary object has in common
with:
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a car moving down the highway at a steady speed, in a
straight line.
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a skydiver who has leapt from an airplane and, a few seconds
later, has reached terminal velocity, meaning he or she is falling
at a steady speed.
The answer is that all three are subject to
balanced forces, although it would appear that their situations have
nothing in common. Anything subject to balanced force is neither
speeding up nor slowing down, nor is it changing direction.
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The stationary object is being accelerated toward the center
of the Earth (i.e., downward) at a rate of 9.81 meters per second
squared (32.17 feet per second squared). But the strength of the
surface it is sitting on opposes the acceleration. Therefore, the
object is not falling. There being no other force acting on it, it
is at rest—at least in the frame of reference of the classroom.
(Someone in space would note that the object is on the surface of
the rotating Earth, which is in turn orbiting the Sun, etc.)
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The car is being accelerated forward by its engine, and that
acceleration is opposed by the friction of the tires on the road,
the air against the car body, and the friction of the parts in the
engine itself. The end result is that the power of the engine, as
applied by the driver, exactly balances the friction opposing the
car, so that it moves at a steady speed.
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The skydiver, like the stationary object, is being
accelerated downward by gravity, but momentarily lacks the support
of a solid surface to counter that acceleration. Like the car, the
skydiver encounters friction, although in this case the friction is
entirely provided by the air, in the form of wind resistance. The
resistance increases with speed. In fact, it soon balances the
acceleration of gravity, so that the skydiver is at terminal
velocity. In a prone, face-down spread-eagle position, this is about
120 miles per hour. After the parachute opens, its increased wind
resistance slows the skydiver to a new terminal velocity of about 12
miles per hour.
Force is action that causes an object to
accelerate. In our examples, the force is provided by gravity (for
the stationary object and the skydiver) and an internal combustion
engine (for the car.)
Force acting to accelerate an object is
typically opposed by its inertia and friction.
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Inertia is an object’s resistance to changes in
velocity or direction, and it increases with the body’s mass. When
an object is already moving with respect to the observer, its
inertia is usually referred to as momentum, and measured as
mass times velocity.
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Friction is the force resisting the movement of two
surfaces in contact with each other.
Here on the surface of the Earth, gravity
and friction tend to drown out all other considerations. For
instance, Newton’s First Law of Motion basically states: An object
at rest tends to remain at rest, and an object in motion tends to
remain in motion, unless acted on by an unbalanced force.
That sums up space travel. But here on
Earth, objects are constantly pressed into contact with each other by
the acceleration of gravity. That contact soon produces enough
friction to stop any motion relative to the friction-producing
surface. Dropped through the air, an object will soon reach terminal
velocity, and a less-dense object (like a feather) will reach it
faster than a denser one (like a stone.) Therefore, the ancients
believed, for instance, that heavier objects fell faster than lighter
objects, since they were not able to consider the question without
air resistance.
Basically, movement on the surface of the
Earth involves using the constant application of force to overcome
friction, as was the case with our example of the car moving down the
highway. Steady acceleration against constant friction keeps it at a
steady speed.
Friction, therefore, dominates our lives, so
that’s what we are going to examine in this lesson, especially the
friction involved in stopping a car.
We rarely can afford the room to just let a
car roll to a stop—we have to apply force in the opposite direction
of travel, resulting in deceleration rather than acceleration. The
standard method involves braking, where the wheels roll slower than
the car’s speed. For braking to actually result in deceleration for
the car, and stop it in the desired road space, there must be
sufficient friction between the rubber wheels and the pavement.
As we are about to see, this cannot
always be assumed.
The amount of friction between two surfaces
is called their coefficient of friction. It is the ratio
between the force required to move an object and its mass. If the
coefficient is 0.5 for a ten-pound object, that means it will take
five pounds of force to move it. (The ratio can be higher than 1.0 if
the surface is sticky.)
Meanwhile, there are several types of
friction. Kinetic friction is the sliding friction for an
object that is already moving. It is the kind of friction that we
have to worry about when stopping a car. Static friction is
the friction of an object that is now at rest but which you are
trying to get into motion.
Kinetic friction for a given surface is
usually lower than its static friction. That is why, if you are
sliding a crate across the floor, it is easier to keep it moving
after you do get it moving. Adding lubricant can reduce kinetic
friction by about 99 percent, and rolling friction can be even less.
There are many sources of friction and there
is no way to calculate what the coefficient of friction for the
interaction of any two surfaces is going to be. It has to be measured
directly. As you might imagine, a lot of effort has gone into making
such measurements, especially concerning tires and roads.
Distribute copies of the Braking Distance
worksheet (S-8-7-1_Braking Distance Worksheet and KEY.doc). Before proceeding, make the following points about
the worksheet:
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The first five coefficients of friction are from various
sources of automotive safety information. The other three are there
for comparison.
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The braking distance formula is credited to the American
Association of State Highway and Transportation Officials, and
assumes a flat road and a vehicle whose brakes are properly
designed, and is not over-loaded or moving at an excessive speed.
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Many factors are involved in braking and this formula cannot
be expected to precisely predict braking distances for specific
situations. But it can serve as a basis for comparison.
Divide the class into teams according to the
number of calculating devices. (If there is only one calculating
device, have students take turns using it to produce results.)
As indicated by the instructions on the
worksheet, each team should use one coefficient of friction to
calculate braking distances for the three different speeds on the
chart. Each student should enter the results on his/her own sheet.
For best results, see that one team uses the
optimal coefficient of friction for the road (0.8) and that another
team uses the coefficient for icy road conditions (0.15). Other teams
should use intermediate coefficients.
Once students are done calculating, lead
them in a discussion of their results. Note these points if no one
else brings them up (S-8-7-1_Braking Distance Worksheet and KEY.doc).
The students can then be asked to discuss
any personal experience they have had involving differing road
conditions leading to differing braking distances.
Extension:
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The exercise refers to braking distance, not stopping
distance. The latter is the complete distance it would take to stop,
counting the braking distance plus the delay that will take place
before the driver begins using the brakes. It can be assumed that
the driver will take at least three-fourths of a second to decide
that there is a problem, and another three-fourths to begin using
the brakes. So have students add the distance traveled in 1.5
seconds at the original velocity to the previously calculated
braking distances.
The Pennsylvania School Bus Driver Training Manual, Unit F,
page 12 (at
www.dmv.state.pa.us/pdotforms/schoolbus_manual/unit_f.pdf
) contains a chart of both braking and stopping distances. It can be
computed that the braking distances all assume the same coefficient
of friction. Using the formula on the Braking Distance Worksheet
(S-8-7-1_Braking Distance Worksheet and KEY.doc), have students calculate what that coefficient of friction
was, and discuss the assumptions that the manual-writer must have
made. (The braking distances are consistent with a coefficient of
friction of 0.67. According to the data on the worksheet, this
assumes the use of moderately worn tires. The manual also assumes a
total reaction time, over and above braking time, of one second.
This assumes an alert, professorial driver.)
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For students performing above and beyond the standards, have
them convert the formula for braking distance into metric units.
This will emphasize unit conversion and provide additional practice
with the concepts imbedded in the formula.