The wheel and axle
The wheel is so common now that it seems impossible to imagine
life without it. Consider some of the many wheels around you and think
what they are mainly used for. You might have thought of wheels on toys,
on a car or bike, a gear wheel, in-line skates, a grinding wheel, a
steering wheel or a potter's wheel. What about a floppy disc?
The wheel in history
The wheel and axle system is a simple machine, used in a multitude
of more complex machines. It has become vital to your everyday life.
People probably used a log to move heavy objects along the ground, or
up ramps, many thousands of years ago.
The first recorded use of a manufactured wheel and axle was on a clay
tablet showing a Sumerian chariot about 3500 BC. The advantage of the
wheel and axle was that it made it easier to carry loads on carts pulled
by people or animals. Since then the wheel has been modified with cogs
to make gear wheels, with buckets to form turbine wheels and becoming
parts of more complex machines.
A mechanical advantage
For a wheel to have value in moving loads there must be some mechanical
advantage. In the case of a wheel and axle the ratio of force (F) to
load (L) is related to the ratio of the radius of the wheel (R) and
that of the axle (r).
In words the mechanical advantage law is that "the force applied
multiplied by the radius of the wheel equals the load multiplied by
the radius of the axle". This can be reduced to F × R = L × r or
L/F = R/r. What this means very simply is that the larger the wheel
relative to the axle the larger the load that can be moved for a given
effort. Hence trucks and buses have bigger wheels than cars!
This is a calculation of the ideal mechanical advantage of the wheel.
The actual mechanical advantage is less because of friction, which causes
loss of energy through thermal energy and sound for example. Friction
can be reduced by lubricated balls in a bearing, but transfer of energy
from a source to a load can never be one hundred percent.
The mechanical advantage law in action
What mechanical advantage is provided by a car steering wheel with a
diameter of about 600 mm and an axle diameter of about 50 mm? First,
knowing that the radius is half the diameter, the radius of the steering
wheel is 300 mm (R) and that of the axle is 25mm (r). The mechanical
advantage of this system is R/r or in this case 300/25 which equals
12. This means that in theory the effort needed to move a load (the
car wheel) is reduced to 1/12 of the weight of the load. Other factors
come into play, such as friction, but you can see that there is a real
advantage with a system like this.
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