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From Wikipedia

Conservative force

A conservative force is a force with the property that the work done in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the net work done (the sum of the force acting along the path multiplied by the distance travelled) by a conservative force is zero.

It is possible to define a numerical value of potential at every point in space for a conservative force. When an object moves from one location to another, the force changes the potential energy of the object by an amount that does not depend on the path taken.

Gravity is an example of a conservative force, while friction is an example of a non-conservative force.

Informal definition

Informally, a conservative force can be thought of as a force that conservesmechanical energy. Suppose a particle starts at point A, and there is a constant force F acting on it. Then the particle is moved around by other forces, and eventually ends up at A again. Though the particle may still be moving, at that instant when it passes point A again, it has traveled a closed path. If the net work done by F at this point is 0, then F passes the closed path test. Any force that passes the closed path test for all possible closed paths is classified as a conservative force.

The gravitational force, spring force, magnetic force (according to some definitions, see below) and electric force (at least in a time-independent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces (in both cases, the energy is converted to heat and cannot be retrieved).

Path independence

A direct consequence of the closed path test is that the work done by a conservative force on a particle moving between any two points does not depend on the path taken by the particle. Also the work done by a conservative force is equal to the negative of change in potential energy during that process. For a proof of that, let's imagine two paths 1 and 2, both going from point A to point B. The variation of energy for the particle, taking path 1 from A to B and then path 2 backwards from B to A, is 0; thus, the work is the same in path 1 and 2, i.e., the work is independent of the path followed, as long as it goes from A to B.

For example, if a child slides down a frictionless slide, the work done by the gravitational force on the child from the top of the slide to the bottom will be the same no matter what the shape of the slide; it can be straight or it can be a spiral. The amount of work done only depends on the vertical displacement of the child.

Mathematical description

A force fieldF, defined everywhere in space (or within a simply-connected volume of space), is called a conservative force or conservative vector fieldif it meets any of these three equivalent conditions:

1. The curl of F is zero:
\nabla \times \vec{F} = 0. \,
2. There is zero net work (W) done by the force when moving a particle through a trajectory that starts and ends in the same place:
W \equiv \oint_C \vec{F} \cdot \mathrm{d}\vec r = 0.\,
3. The force can be written as the gradient of a potential, \Phi:
\vec{F} = -\nabla \Phi. \,

The term conservative force comes from the fact that when a conservative force exists, it conserves mechanical energy. The most familiar conservative forces are gravity, the electric force (in a time-independent magnetic field, see Faraday's law), and spring force.

Many forces (particularly those that depend on velocity) are not force fields. In these cases, the above three conditions are not mathematically equivalent. For example, the magnetic force satisfies condition 2 (since the work done by a magnetic field on a charged particle is always zero), but does not satisfy condition 3, and condition 1 is not even defined (the force is not a vector field, so one cannot evaluate its curl). Accordingly, some authors classify the magnetic force as conservative, while others do not. The magnetic force is an unusual case; most velocity-dependent forces, such as friction, do not satisfy any of the three conditions, and therefore are unambiguously nonconservative.

Nonconservative forces

Nonconservative forces can only arise in classical physics due to neglected degrees of freedom. For instance, friction may be treated without resorting to the use of nonconservative forces by considering the motion of individual molecules; however that means every molecule's motion must be considered rather than handling it through statistical methods. For macroscopic systems the nonconservative approximation is far easier to deal with than millions of degrees of freedom. Examples of nonconservative forces are friction and non-elastic material stress.

However, general relativity is non-conservative, as seen in the anomalous precession of Mercury's orbit. However, general relativity can be shown to conserve a stress-energy-momentum pseudotensor.

Fictitious force

A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial frame of reference, such as a rotating reference frame.

The force F does not arise from any physical interaction but rather from the acceleration a of the non-inertial reference frame itself. As stated by Iro:

According to Newton's second law in the form F = ma, fictitious forces always are proportional to the mass m acted upon.

Four fictitious forces are defined in accelerated frames: one caused by any relative acceleration of the origin in a straight line (rectilinear acceleration), two caused by any rotation (centrifugal force and Coriolis force) and a fourth, called the Euler force, caused by a variable rate of rotation, should that occur.


The role of fictitious forces in Newtonian mechanics is described by Tonnelat:

Fictitious forces on Earth

The surface of the Earth is a rotating reference frame. To solve classical mechanics problems exactly in an Earth-bound reference frame, three fictitious forces must be introduced, the Coriolis force, the centrifugal force (described below) and the Euler force. The Euler force is typically ignored because its magnitude is very small. Both of the other fictitious forces are weak compared to most typical forces in everyday life, but they can be detected under careful conditions. For example, Léon Foucault was able to show the Coriolis force that results from the Earth's rotation using the Foucault pendulum. If the Earth were to rotate a thousand times faster (making each day only ~86 seconds long), people could easily get the impression that such fictitious forces are pulling on them, as on a spinning carousel.

Detection of non-inertial reference frame

Observers inside a closed box that is moving with a constant velocity cannot detect their own motion; however, observers within an accelerating reference frame can detect that they are in a non-inertial reference frame from the fictitious forces that arise. For example, for straight-line acceleration:

Other accelerations also give rise to fictitious forces, as described mathematically below. The physical explanation of motions in an inertial frames is the simplest possible, requiring no fictitious forces: fictitious forces are zero, providing a means to distinguish inertial frames from others.

An example of the detection of a non-inertial, rotating reference frame is the precession of a Foucault pendulum. In the non-inertial frame of the Earth, the fictitious Coriolis force is necessary to explain observations. In an inertial frame outside the Earth, no such fictitious force is necessary.

Examples of fictitious forces

Acceleration in a straight line

Figure 1 (top) shows an accelerating car. When a car accelerates hard, the common human response is to feel "pushed back into the seat." In an inertial frame of reference attached to the road, there is no physical force moving the rider backward. However, in the rider's non-inertial reference frame attached to the accelerating car, there is a backward fictitious force. We mention two possible ways of analyzing the problem:

  1. Figure 1, (center panel). From the viewpoint of an inertial reference frame with constant velocity matching the initial motion of the car, the car is accelerating. In order for the passenger to stay inside the car, a force must be exerted on the passenger. This force is exerted by the seat, which has started to move forward with the car and is compressed against the passenger until it transmits the full force to keep the passenger moving with the car. Thus, the passenger is accelerating in this frame due to the unbalanced force of the seat.
  2. Figure 1, (bottom panel). From the point of view of the interior of the car, an accelerating reference frame, there is a fictitious force pushing the passenger backwards, with magnitude equal to the mass of the passenger times the acceleration of the car. This force pushes the passenger back into the seat, until the seat compresses and provides an equal and opposite force. Thereafter, the passenger is stationary in this frame, because the fictitious force and the (real) force of the seat are balanced.

How can the accelerating frame be discovered to be non-inertial? In the accelerating frame, everything appears to be subject to zero net force, and nothing moves. Nonetheless, compression of the seat is observed and is explained in the accelerating frame (and in an inertial frame) because the seat is subject to the force of acceleration from the car on one side, and the opposing force of reaction to acceleration by the passenger on the other. Identification of the accelerating frame as non-inertial cannot be based simply on the compression of the seat, which all observers can explain; rather it is based on the simplicity of the physical explanation for this compression.

The explanation of the seat compression in the accelerating frame requires not only the thrust from the axle of the car, but additional (fictitious) forces. In an inertial frame, only the thrust from the axle is necessary. Therefore, the inertial frame has a simpler physical explanation (not necessarily a simpler mathematical formulation, however), indicating the accelerating frame is a non-inertial frame of reference. In other words, in the inertial frame, fictitious forces are zero. See inertial frame for more detail.

This example illustrates how fictitious forces arise from switching from an inertial to a non-inertial reference frame. Calculations of physical quantities (compression of the seat, required force from the axle) made in any frame give the same ans

Task force

A task force (TF) is a unit or formation established to work on a single defined task or activity. Originally introduced by the United States Navy, the term has now caught on for general usage and is a standard part of NATO terminology. Many non-military organizations now create "task forces" or task groups for temporary activities that might have once been performed by ad hoc committees.

Types of task forces

Joint Task Force

In U.S. terminology, now widely adopted, including by NATO, the term Joint implies the combination of more than one military service (i.e. some combination of army, naval and/or air forces). Therefore a Joint Task Force (JTF) is a TF which includes more than one service.

United States Department of Defense

A joint task force (JTF) is a joint force that is constituted and so designated by a JTF establishing authority. A JTF establishing authority may be the Secretary of Defense or the commander of a combatant command, subordinate unified command, or existing JTF. In most situations, the JTF establishing authority will be a combatant commander. JTFs are established on a geographical area or functional basis when the mission has a specific limited objective and does not require overall centralized control of logistics.

Examples include Joint Task Force Bravo, Joint Task Force Guantanamo, Joint Task Force Lebanon, and Joint Task Force-Global Network Operations.


Joint Task Force 2 (JTF2) is the Canadian Forces' elite special forces unit. However, it is not temporary but permanent, and does not fit with the US Combined Communication-Electronics Board system (TF 2 remains allocated to the United States). Thus while it is called a Joint Task Force and it does involve personnel from all three services (Army, Navy, and Air Force, therefore "Joint") it is not temporary (therefore not a "Task Force" by the US definition). It is known to have fought in Afghanistan and was part of the United Nations Stabilization Mission in Haiti.

Combined Task Force

In U.S. terminology, now widely adopted, including by NATO, the term combined implies more than one nation. At the start of World War II, the UK used "Combined" to denote forces composed of more than one service, which is how the Combined Operations term originated. However they soon adopted the U.S. usage, and organizations were named accordingly, for example, the Combined Chiefs of Staff. Today a Combined Task Force (CTF) is a task force which includes sub-elements of more than one nation.

An example is Combined Task Force 151.

Combined Joint Task Force

A Combined Joint Task Force (CJTF) is a task force which includes elements of more than one service and elements of more than one nation. Examples include Combined Joint Task Force 76 and Task Force Viking.


The concept of a naval task force is as old as navies, but the term came into extensive use originally by the United States Navy around the beginning of 1941, as a way to increase operational flexibility. Prior to that time the assembly of ships for naval operations was referred to as fleets, divisions, or on a smaller scale, squadrons, and flotillas.

Before the Second World War ships were collected in divisions derived from the Royal Navy's "division" of the line of battle in which one squadron usually remained under the direct command of the Admiral of the Fleet, one squadron was commanded by a Vice Admiral and one by a Rear Admiral, each of the three squadrons flying different coloured flags, hence the terms flagship and flag officer. The flag of the Fleet Admiral's squadron was red, the Vice Admiral's was white and the Rear Admiral's blue. (The names "Vice" (from advanced) and "Rear" may have derived from sailing positions within the line at the moment of engagement.) In the late 19th century ships were collected in numbered squadrons, which were assigned to named (such as the Asiatic Fleet) and later numbered fleets.

A task force can be assembled using ships from different divisions and squadrons, without requiring a formal and permanent fleet reorganization, and can be easily dissolved following completion of the operational task. The task force concept worked very well, and by the end of World War II about 100 task forces had been created in the United States Navy alone.

United States Navy

These are temporary call signs designated to particular ship/ships assigned to fulfill certain missions. CTF can be read as Commander Task force while TF is Task Force. Likewise the force is broken down as following: task force, task g


A kilogram-force (kgf), or kilopond (kp, from latin pondus meaning weight), is an informal unit of force equal to the magnitude of the force exerted on one kilogram of mass by a gravitational field (standard gravity, a conventional value approximating the average magnitude of gravity on Earth). Therefore one kilogram-force is by definition equal to newtons. Similarly, a gram-force is millinewtons (or newtons), and a milligram-force is micronewtons (or newton).

The kilogram-force has never been a part of the International System of Units (SI), which was introduced in 1960. The SI unit of force is the newton.

Prior to this, the unit was widely used in much of the world; it is still in use for some purposes. The thrust of a rocket engine, for example, was measured in kilograms-force in 1940s Germany, in the Soviet Union (where it remained the primary unit for thrust in the Russian space program until at least the late 1980s), and it is still used today in China and sometimes by the European Space Agency.

It is also used for tension of bicycle spokes, for torque measured in "meter-kilograms", for informal references to pressure in kilograms per square centimeter, for the draw weight of bows in archery, and to define the "metric horsepower" (PS) as 75 metre-kiloponds per second.

The gram-force and kilogram-force were never well-defined units until the CGPM adopted a standard acceleration of gravity of 980.665 cm/s2 for this purpose in 1901, though they had been used in low-precision measurements of force before that time.

A tonne-force, metric ton-force, megagram-force, or megapond (Mp) are 1000 kilograms-force.

The decanewton or dekanewton (daN) is used in some fields as an approximation to the kilogram-force, being exactly rather than approximately 10 newtons.

From Yahoo Answers

Question:i'm doing a project and i need to find out What are common disease/injuries to the muscular system? How are they caused?

Answers:They are commonly referred to as soft tissue injuries if they are the result of trauma (forces acting on the body). Then there are atrophy types of disorders where the muscles waste away from lack of use or from muscular dystrophy. There are many many things that can have a debilitating effect on muscle tissue. This is a big topic and is hard to cover in this forum

Question:I'm thinking about joining, since I'm 22, and if I don't get in shape now, it'll be impossible when I'm older

Answers:yep. They'll force you to work out even when you're feeling lazy. If you get deployed you'll have a lot of time to workout.


Answers:Force / Mass= Acceleration

Question:Express "nowton" in terms of base unit.

Answers:as dimension it is f = m * a [m]= M [ a ] = LT^-2 so [ f ] = M L T ^ -2 or f if kg . m / s^2 or pa . m^2

From Youtube

Precalculus - Components of a Force :Free Math Help at Brightstorm! www.brightstorm.com How to define the components of a vector.

Magnetic Force from the Lorentz Force Law :The magnetic field B is defined from the Lorentz Force Law, and specifically from the magnetic force on a moving charge. The implications of this expression include: 1. The force is perpendicular to both the velocity v of the charge q and the magnetic field B. 2. The magnitude of the force is F = qvB sin where is the angle smaller than 180 degrees between the velocity and the magnetic field. This implies that the magnetic force on a stationary charge or a charge moving parallel to the magnetic field is zero. 3. The direction of the force is given by the right hand rule. The force relationship above is in the form of a vector product. From the force relationship above it can be deduced that the units of magnetic field are Newton seconds /(Coulomb meter) or Newtons per Ampere meter. This unit is named the Tesla. It is a large unit, and the smaller unit Gauss is used for small fields like the Earth's magnetic field. A Tesla is 10000 Gauss. The Earth's magnetic field is on the order of half a Gauss. Courtesy: hyperphysics.phy-astr.gsu.edu