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## PowerPedia:Force

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In Physics, force is that which changes or tends to change the state of rest or motion of a body. It is an influence that may cause a body to There was an error working with the wiki: Code[29]. The actual acceleration of the body is determined by the sum of all forces acting on it (known as There was an error working with the wiki: Code[30] or resultant force). Force is a There was an error working with the wiki: Code[31] defined as the rate of change of the There was an error working with the wiki: Code[32] of the body that would be induced by that force acting alone. Since There was an error working with the wiki: Code[32] is a vector, the force has a direction associated with it. The SI unit of force is the There was an error working with the wiki: Code[34], while the English unit of force is the There was an error working with the wiki: Code[35]. As well as causing acceleration (a change in the body's change of motion) a force may also cause the body to distort (There was an error working with the wiki: Code[36]) or turn (There was an error working with the wiki: Code[37]), thereby changing the body's state of rest.

#### History

Force was first described by Archimedes.

There was an error working with the wiki: Code[38] used rolling balls to disprove the There was an error working with the wiki: Code[39] (There was an error working with the wiki: Code[40] - There was an error working with the wiki: Code[41])

There was an error working with the wiki: Code[42] is credited for giving the first mathematical definition of force.

There was an error working with the wiki: Code[43] is credited for experimental discovery of the inverse square law of interaction between Electric charges using There was an error working with the wiki: Code[44] (There was an error working with the wiki: Code[45]).

There was an error working with the wiki: Code[46]'s There was an error working with the wiki: Code[47] measured the force of gravity between two masses (There was an error working with the wiki: Code[48])

Ancient writers, such as There was an error working with the wiki: Code[49], failed to appreciate that most ordinary objects do not move because they are in the grip of opposing but equal forces. Aristotle and others believed that it was the natural state of objects on Earth to be motionless, and that they tended toward that state (eventually settling down to inertness), if left alone. This was a common experience of humans with ordinary conditions in which friction was involved, so Newton's idea that unopposed forces naturally produce constant increases in velocities, was not an obvious one. Frictional forces, acting in opposition to other kinds of forces, historically tended to hide the correct mathematical relationship between simple unopposed force and motion.

The correct behavior for unopposed forces was first discovered by There was an error working with the wiki: Code[50] in working with gravity, although it was not until Newton that gravity was seen as simply producing one kind of unopposed "force". Newton generalized the behavior of constant acceleration, or constant momentum gain, to forces other than gravity. He asserted in his second law of motion that this behavior of constant momentum increase was characteristic of all forces-- including the "forces" of ordinary experience, such as tension or the stress produced by pushing on an object with a finger.

#### Examples

A heavy object on a table is pulled (attracted) downward toward the floor by the force of gravity (i.e., its weight). At the same time, the table resists the downward force with equal upward force (called the There was an error working with the wiki: Code[51]), resulting in zero net force, and no acceleration. (If the object is a person, he actually feels the normal force acting on him from below.)

A heavy object on a table is gently pushed in a sideways direction by a finger. However, it fails to accelerate sideways, because the force of the finger on the object is now opposed by a new force of There was an error working with the wiki: Code[52], generated between the object and the table surface. This newly generated force exactly balances the force exerted on the object by the finger, and again no acceleration occurs. The static friction increases or decreases automatically. If the force of the finger is increased (up to a point), the opposing sideways force of static friction increases exactly to the point of perfect opposition.

A heavy object on a table is pushed by a finger hard enough that static friction cannot generate sufficient force to match the force exerted by the finger, and the object starts sliding across the surface. If the finger is moved with a constant velocity, it needs to apply a force that exactly cancels the force of There was an error working with the wiki: Code[53] from the surface of the table and then the object moves with the same constant velocity. Here it seems to the naive observer that application of a force produces a velocity (rather than an acceleration). However, the velocity is constant only because the force of the finger and the kinetic friction cancel each other. Without friction, the object would continually accelerate in response to a constant force.

A heavy object reaches the edge of the table and falls. Now the object, subjected to the constant force of its weight, but freed of the normal force and friction forces from the table, gains in velocity in direct proportion to the time of fall, and thus (before it reaches velocities where air resistance forces becomes significant compared to gravity forces) its rate of gain in momentum and velocity is constant. These facts were first discovered by There was an error working with the wiki: Code[54].

#### Quantitative definition

According to There was an error working with the wiki: Code[1], the force is equal to the rate of change of momentum with time:

: {F} = {d{p} \over dt}.

The quantity {p} = m {v} (where m\, is the Mass and {v} is the Velocity) is called the There was an error working with the wiki: Code[55]. If the mass m is constant in time, then Newton's law can be written in the simplified form

: {F} = \frac{d{p}}{dt}= \frac{d(m{v})}{dt} = m\frac{d({v})}{dt} = m{a}

where a = {d v} /{dt} is the There was an error working with the wiki: Code[56].

This is the form Newton's second law is usually taught in introductory physics courses in order to avoid calculus notation.

All known forces of nature are defined via the above Newtonian definition of force. For example, weight (force of gravity) is defined as mass times acceleration of free fall: w = mg spring balance force is defined as the force equilibrating certain gravitational force (say, the weight of 1 kg mass near Earth surface results in reaction force of spring equivalent to 9.8 N), etc. Calibration of spring balances (of various kinds) using either gravitational force or motion with known acceleration is important starting procedure in measuring many other forces (such as friction forces, reaction forces, electric forces, magnetic force, etc) in various physics labs.

It is not always the case that m is independent of t. For example, the mass of a There was an error working with the wiki: Code[57] decreases as its propellant is ejected. Under such circumstances, the above equation ({F} = m{a} ) is incorrect, and the original form of Newton's second law must be used.

The relation {F} = m{a} also fails to hold as velocity approaches the speed of light, in accordance with the There was an error working with the wiki: Code[2], although the basic definition {F} = d{p}/dt is still valid.

Because momentum is a There was an error working with the wiki: Code[3], then force, being its time derivative, is also a vector - it has There was an error working with the wiki: Code[4]s. When two forces act on an object, the resulting force, the resultant, is the There was an error working with the wiki: Code[5] of the original forces. This is called the principle of There was an error working with the wiki: Code[58]. The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action. As with all vector addition this results in a There was an error working with the wiki: Code[59]: the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector which is equal in magnitude and direction to the transversal of the parallelogram. If the two forces are equal in magnitude but opposite in direction, then the resultant is zero. This condition is called There was an error working with the wiki: Code[60], with the result that the object remains at its constant velocity (which could be zero). Static equilibrium is mathematically equivalent to the motion expected with equal and oppositely directed There was an error working with the wiki: Code[61]s (of course it is the same motion as with no acceleration).

As well as being added, forces can also be broken down (or 'resolved'). For example, a horizontal force pointing northeast can be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields the original force. Force vectors can also be three-dimensional, with the third (vertical) component at right-angles to the two horizontal components.

In most explanations of There was an error working with the wiki: Code[62], force is usually defined only implicitly, in terms of the equations that work with it. Some physicists, philosophers and mathematicians, such as There was an error working with the wiki: Code[63], There was an error working with the wiki: Code[64] and There was an error working with the wiki: Code[65], have found this problematic and sought a more explicit definition of force.

#### Force and potential

Instead of a force, the mathematically equivalent concept of a There was an error working with the wiki: Code[6]), a potential field U(r) is defined as that field whose There was an error working with the wiki: Code[66] is equal and opposite to the force produced at every point:

:\textbf{F}=-\nabla U

Forces can be classified as There was an error working with the wiki: Code[7] or nonconservative. Conservative forces are equivalent to the There was an error working with the wiki: Code[8] force, and There was an error working with the wiki: Code[9] force. Nonconservative forces include There was an error working with the wiki: Code[10]. However, for any sufficiently detailed description, all forces are conservative.

#### Types of force

Many forces exist: the There was an error working with the wiki: Code[11] (between There was an error working with the wiki: Code[12] (between There was an error working with the wiki: Code[13], There was an error working with the wiki: Code[14] forces (in There was an error working with the wiki: Code[15], Magnetism, There was an error working with the wiki: Code[16], There was an error working with the wiki: Code[67] and There was an error working with the wiki: Code[68]s to name a few.

Only four There was an error working with the wiki: Code[17], the There was an error working with the wiki: Code[18]. All other forces can be reduced to these fundamental interactions.

The modern quantum mechanical view of the first three fundamental forces (all except gravity) is that particles of matter (There was an error working with the wiki: Code[69]) do not directly interact with each other but rather by exchange of There was an error working with the wiki: Code[70] (There was an error working with the wiki: Code[71]) (as, for example, virtual There was an error working with the wiki: Code[72] in case of interaction of There was an error working with the wiki: Code[73]).

In There was an error working with the wiki: Code[74], Gravitation is not strictly viewed as a force. Rather, objects moving free in gravitational fields (say, a basket ball) simply undergo There was an error working with the wiki: Code[75] along a straight line in the There was an error working with the wiki: Code[76] (straight line in curved space-time is defined as the shortest space-time path between two points, and it is called There was an error working with the wiki: Code[77]). This straight line in space-time is a curved line in space, and we call it "There was an error working with the wiki: Code[78]" of object (say, a There was an error working with the wiki: Code[79] for a basket ball moving in a uniform gravitational field). The time derivative of changing momentum of that body is what we label as "gravitational force" (=There was an error working with the wiki: Code[80]). There was an error working with the wiki: Code[81] (which has no mass but has Energy and There was an error working with the wiki: Code[82] in its e/m field) also propagates in gravitational field along a straight space-time path (geodesic).

#### Units of measurement

The There was an error working with the wiki: Code[19] engineering units, if F is measured in "There was an error working with the wiki: Code[20]" or "lbf", and a in feet per second squared, then m must be measured in There was an error working with the wiki: Code[21]s. Similarly, if mass is measured in There was an error working with the wiki: Code[22], and a in feet per second squared, the force must be measured in There was an error working with the wiki: Code[83]s. The units of There was an error working with the wiki: Code[84] and There was an error working with the wiki: Code[83]s are specifically designed to avoid a constant of proportionality in this equation.

A more general form F=k·m·a is needed if consistent units are not used. Here, the constant k is a conversion factor dependent upon the units being used.

When the standard There was an error working with the wiki: Code[23] (an acceleration of 9.80665 m/s²) is used to define pounds force, the mass in pounds is numerically equal to the weight in pounds force. However, even at sea level on Earth, the actual acceleration of free fall is quite variable, over 0.53% more at the poles than at the equator. Thus, a mass of 1.0000 lb at sea level at the equator exerts a force due to gravity of 0.9973 lbf, whereas a mass of 1.000 lb at sea level at the poles exerts a force due to gravity of 1.0026 lbf. The normal average sea level acceleration on Earth (World Gravity Formula 1980) is 9.79764 m/s², so on average at sea level on Earth, 1.0000 lb will exerts a force of 0.9991 lbf.

The equivalence 1 lb = 0.453&nbsp592&nbsp37 kg is always true, by definition, anywhere in the universe. If you use the standard There was an error working with the wiki: Code[24] which is official for defining kilograms force to define pounds force as well, then the same relationship will hold between pounds-force and kilograms-force (an old non-SI unit is still used). If a different value is used to define pounds force, then the relationship to kilograms force will be slightly different&mdashbut in any case, that relationship is also a constant anywhere in the universe. What is not constant throughout the universe is the amount of force in terms of pounds-force (or any other force units) which 1 lb will exert due to gravity.

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 There was an error working with the wiki: Code[25]. An item with a mass of 10 kg has a mass of 1.01972661 metric slugs (= 10 kg divided by 9.80665 kg per metric slug). This unit is also known by various other names such as the There was an error working with the wiki: Code[26], TME (from a German acronym), and mug (from metric slug).

Another unit of force called the There was an error working with the wiki: Code[86] (pdl) is defined as the force that accelerates 1 lbm at 1 foot per second squared. Given that 1 lbf = 32.174 lb times one foot per second squared, we have 1 lbf = 32.174 pdl.

The There was an error working with the wiki: Code[87] is a unit of force that was used in various fields of science and technology. In 1901, the There was an error working with the wiki: Code[88] improved the definition of the kilogram-force, adopting a standard acceleration of gravity for the purpose, and making the kilogram-force equal to the force exerted by a mass of 1 kg when accelerated by 9.80665 m/s². The kilogram-force is not a part of the modern SI system, but is still used in applications such as:

Thrust of Jet engine and There was an error working with the wiki: Code[89]s

Spoke tension of There was an error working with the wiki: Code[90]s

Draw weight of There was an error working with the wiki: Code[27]

There was an error working with the wiki: Code[91]es in units such as "meter kilograms" or "kilogram centimetres" (the kilograms are rarely identified as units of force)

Engine torque output (kgf·m expressed in various word orders, spellings, and symbols)

Pressure gauges in "kg/cm²" or "kgf/cm²"

In colloquial, non-scientific usage, the "kilograms" used for "weight" are almost always the proper SI units for this purpose. They are units of mass, not units of force.

The symbol "kgm" for kilograms is also sometimes encountered. This might occasionally be an attempt to disintinguish kilograms as units of mass from the "kgf" symbol for the units of force. It might also be used as a symbol for those obsolete torque units (kilogram-force metres) mentioned above, used without properly separating the units for kilogram and metre with either a space or a centered dot.

##### Conversions

Below are several conversion factors between various measurements of force:

1 dyne = 10-5 newtons

1 kgf (kilopond kp) = 9.80665 newtons

1 There was an error working with the wiki: Code[28] = 9.80665 kg

1 lbf = 32.174 poundals

1 slug = 32.174 lb

1 kgf = 2.2046 lbf

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Torque

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#### References and external articles

Parker, Sybil, Encyclopedia of Physics, p 443, Ohio McGraw-Hill 1993, ISBN 0-07-051400-3

Corbell, H.C. Philip Stehle, Classical Mechanics p 28, New York, Dover publications, 1994, ISBN 0-486-68063-0

Halliday, David, Robert Resnick Kenneth S. Krane, Physics v. 1, New York, John Wiley & Sons, 2001, ISBN 0-471-32057-9

Serway, Raymond A., Physics for Scientists and Engineers, Philadelphia, Saunders College Publishing 2003 ISBN 0-534-40842-7

Tipler, Paul, Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics, 5th ed. W. H. Freeman 2004 ISBN 0-7167-0809-4

There was an error working with the wiki: Code[1], Wikipedia: The Free Encyclopedia. Wikimedia Foundation.