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Force
Force
Force isn't really a fundamental quantity in physics, despite
the inertia of physics education still introducing students to physics via the
Newtonian concept of force. More fundamental are momenta, energy and stress. In
fact, no one measures force directly. Instead, everytime one says one is
measuring a force, a quick rethinking would make one realize that what one
really measures is stress (or maybe its gradient). The "force" you feel on your
skin, for example, is really your pressure nerve cells picking up a change in
pressure. A spring meter measures the tension of the spring, which is really its
stress, etc. etc.
In
physics, a net force acting on a body causes that body to
accelerate (i.e. to change its
velocity). Force is a
vector. The
SI unit used to measure force is the
newton.
See also engineering
mechanics:
-
Statics Where the sum of the forces acting on a body in static equilibrium
(motionless, Acceleration=0) is zero. F=MA=0
-
Dynamics The sum of the forces acting on a body or system over time is non
zero with a resulting set of accelerations defined by detailed analysis of
equations derived from F=MA.
Force was first described by
Archimedes. The total (Newtonian)
force on a point particle at a certain instant in a specified situation is
defined as the rate of change of its
momentum:
-
Where m is the
inertial mass of the particle, vo is its initial
velocity, v is its final velocity, and T is the time from the initial state
to the final state; the expression on the right of the equation being the limit
as T goes to zero.
Force was so defined in order that its
reification would explain the effects of superimposing situations: If in one
situation, a force is experienced by a particle, and if in another situation
another force is experience by that particle, then in a third situation, which
(according to standard physical practice) is taken to be a combination of the
two individual situations, the force experienced by the particle will be the
vector sum of the individual forces experienced in the first two situations.
This superposition of forces, along with the definition of
inertial frames and
inertial mass, are the empirical content of
Newton's laws of motion.
Since force is a vector it can be resolved into components.
For example, a 2D force acting in the direction North-East can be split in to
two forces along the North and East directions respectively. The vector-sum of
these component forces is equal to the original force.
The content of above definition of force can be further
explicated. First, the mass of a body times its velocity is designated its
momentum (labeled p). So the above definition can be written:
-
If F is not constant over Δt, then this is the
definition of average force over the time interval. To apply it at an instant we
apply an idea from
Calculus. Graphing p as a function of time, the average force will be
the slope of the line connecting the momentum at two times. Taking the limit as
the two times get closer together gives the slope at an instant, which is called
the derivative:
-
With many forces a
potential energy field is associated. For instance, the gravitational force
acting upon a body can be seen as the action of the
gravitational field that is present at the body's location. The potential
field is defined as that field whose
gradient is minus the force produced at every point:
-
While force is the name of the derivative of
momentum with respect to time, the derivative of force with respect to time
is sometimes called
yank.
Higher order derivates can be considered, but they lack names, because they are
not commonly used.
In most expositions of
mechanics, force is usually defined only implicitly, in terms of the
equations that work with it. Some physicists, philosophers and mathematicians,
such as
Ernst Mach,
Clifford Truesdell and
Walter Noll, have found this problematic and sought a more explicit
definition of force.
In the relationship
-
F = m×a,
which is derived from
Newton’s second law of motion, F is the force in newtons, m
the mass in kilograms and a the acceleration in meters per second
squared. To a physicist, the kilogram is a unit of
mass,
but in common usage "kilogram" is a shorthand for "the weight of a one kilogram
mass at sea level on earth". At sea level on earth, the acceleration due to
gravity (a in the above equation) is 9.807 meters per second squared,
so the weight of one kilogram is 1 kg × 9.807 m/s² = 9.807 N.
To distinguish these two meanings of "kilogram", the
abbreviations "kgm" for kilogram mass (i.e. 1 kg) and "kgf" for kilogram force,
also called kilopond (kp), equal to 9.807 N, are sometimes used. These are only
informal terms and are not recognized in the SI system of units.
The relationship F = m×a mentioned above may also be used
with non-metric units.
For example, in imperial engineering units, F is in “pounds
force” or "lbf", m is in "pounds mass" or "lbm", and a is in
feet per second squared.
As with the kilogram, the pound is colloquially used as both
a unit of mass and a unit of force or weight. 1 lbf is the force required to
accelerate 1 lbm at 32.174 ft per second squared, since 32.174 ft per second
squared is the acceleration due to terrestrial gravity at sea level.
Another imperial unit of mass is the slug, defined as 32.174
lbm. It is the mass that accelerates by one foot per second squared when a force
of one lbf is exerted on it.
At sea level on earth, the magnitude of lbm exactly equals
the magnitude of lbf, and the magnitude of kgm exactly equals the magnitude of
kgf. This equivalency is only true at the surface of the earth, and does not
hold up when acceleration other than that of the standard acceleration of
gravity (that at the sea level of Earth) is used.
In other words, your mass and force exerted on the ground
equal the same number in pounds (that is, lbm and lbf) on Earth at sea level.
Since kgf and lbf are units of force, they are invariant, and the equivalence 1
kgf = 2.2046 lbf is always true. However, the conversion 1 kgm = 2.2046 lbm is
true only on Earth at sea level.
The concept of weight, unlike force and mass, depends on the
environment in which the weighing is done. It can be assumed that this is at sea
level on Earth, unless other conditions are stated. Thus one pound mass (lbm)
weighs one pound (lbf), and one kilogram mass (kgm) weighs one kilogram force (kgf).
Further, an item with a weight of 10 lbf has a mass of 10 lbm and also a mass of
0.3108 slugs (= 10 lbm divided by 31.174 lbm per slug).
By analogy with the slug, there is a rarely used unit of mass
called the "metric slug". This is the mass that accelerates at one metre per
second squared when pushed by a force of one kgf. An item with a weight (on
Earth at sea level) of 10 kgf has a mass of 10 kgm and also a mass of 1.0197
metric slugs (= 10 kgm divided by 9.807 kgm per metric slug).
An even rarer unit of force called the "imperial newton" is
defined as the force that accelerates 1 lbm at 1 foot per second squared. Given
that 1 lbf = 32.174 lbm times one foot per square second, we have (1/32.174 =)
0.0311 lbf = 1 lbm times 1 foot per square second = 1 imperial newton. Thus 1
lbf = 32.174 imperial newtons.
In conclusion, we have the following conversions, with
“metric slugs” used very infrequently, and “imperial newtons” virtually never
used.
1 kgf = 9.807 newton 1 metric slug = 9.807 kgm
1 lbf = 32.174 imperial newtons 1 slug = 32.174 lbm
1 kgf = 2.2046 lbf
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