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Contact force

In physics, a contact force is a force between two objects (or an object and a surface) that are in contact with each other. This is distinct from a non-contact force, or action-at-a-distance force (a force that acts over a distance), such as gravity or magnetic attraction/repulsion. Contact forces always exist in pairs of equal in magnitude but opposite in direction forces, by Newton's third law.

A contact force can be split into two components. The part of the force that lies within the plane of contact is friction, which must be overcome for the two objects to slide relative to one another along that plane. The part of the force that is perpendicular to the plane of contact is called the normal force. Friction is proportional to the normal contact force, and the constant of proportionality is denoted by the term μ (mu).

Strictly speaking, contact forces are only a useful simplification for introductory physics classes and other applications of classical mechanics. Everyday objects on Earth do not actually touch each other; rather contact forces are the result of the interactions of the electrons at or near the surfaces of the objects (exchange interaction).


An example of contact force commonly encountered in college-level physics is the force between two masses A and B which are lying next to each other and a force F is being applied on one of the masses, for example A. In such a case, the contact force will be proportional to the mass of B.

Hence, we can see the many examples of contact forces in everyday life. Contact forces can act through a rigid connector or a non rigid connector .

For example when a boy pulls a cart through a rope he is connecting the force applied through a non rigid connector(the rope) He could also pull the cart through the handle of the cart hence transferring the force through the rigid connector (the handle)

But from case A the boy cannot push the cart(disadvantage of non rigid connector )

From this investigation we can prove that: a rigid connector can push or pull but a non rigid connector can only pull .

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.

Non-Newtonian fluid

A non-Newtonian fluid is a fluid whose flow properties differ in any way from those of Newtonian fluids. Most commonly the viscosity of non-Newtonian fluids is not independent of shear rate or shear rate history. However, there are some non-Newtonian fluids with shear-independent viscosity, that nonetheless exhibit normal stress-differences or other non-Newtonian behavior. Many salt solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as ketchup, custard, toothpaste, starch suspensions, paint, blood, and shampoo. In a Newtonian fluid, the relation between the shear stress and the shear rate is linear, passing through the origin, the constant of proportionality being the coefficient of viscosity. In a non-Newtonian fluid, the relation between the shear stress and the shear rate is different, and can even be time-dependent. Therefore a constant coefficient of viscosity cannot be defined.

Although the concept of viscosity is commonly used to characterize a material, it can be inadequate to describe the mechanical behavior of a substance, particularly non-Newtonian fluids. They are best studied through several other rheological properties which relate the relations between the stress and strain rate tensors under many different flow conditions, such as oscillatory shear, or extensional flow which are measured using different devices or rheometers. The properties are better studied using tensor-valued constitutive equations, which are common in the field of continuum mechanics.

Types of non-Newtonian behavior


Shear thickening fluids

Shear thickening fluids are also used in all wheel drive systems utilising a viscous coupling unit for power transmission.

Shear thinning fluid

A familiar example of the opposite, a shear thinning fluid, or pseudoplastic fluid, is paint: one wants the paint to flow readily off the brush when it is being applied to the surface being painted, but not to drip excessively.

Bingham plastic

There are fluids which have a linear shear stress/shear strain relationship which require a finite yield stress before they begin to flow (the plot of shear stress against shear strain does not pass through the origin). These fluids are called Bingham plastics. Several examples are clay suspensions, drilling mud, toothpaste, mayonnaise, chocolate, and mustard.


There are also fluids whose strain rate is a function of time. Fluids that require a gradually increasing shear stress to maintain a constant strain rate are referred to as rheopectic. An opposite case of this, is a fluid that thins out with time and requires a decreasing stress to maintain a constant strain rate (thixotropic).



An inexpensive, non-toxic example of a non-Newtonian fluid is a suspension of starch (e.g. cornflour) in water, sometimes called "oobleck" or "ooze" (2 parts corn starch to 1 part water). Uncooked imitation custard, being a suspension of primarily cornflour, has the same properties. The name "oobleck" is derived from the children's book Bartholomew and the Oobleck.


Flubber is a non-Newtonian fluid, easily made from polyvinyl alcohol based glues and borax, that flows under low stresses, but breaks under higher stresses and pressures. This combination of fluid-like and solid-like properties makes it a Maxwell solid. Its behavior can also be described as being viscoplastic or gelatinous.

Chilled caramel topping

Another example of this is chilled caramel ice cream topping. The sudden application of force—for example by stabbing the surface with a finger, or rapidly inverting the container holding it—leads to the fluid behaving like a solid rather than a liquid. This is the "shear thickening" property of this non-Newtonian fluid. More gentle treatment, such as slowly inserting a spoon, will leave it in its liquid state. Trying to jerk the spoon back out again, however, will trigger the return of the temporary solid state. A person moving quickly and applying sufficient force with their feet can literally walk across such a liquid.

Silly Putty

Silly Putty is a silicone polymer based suspension which will flow, bounce, or break depending on strain rate.


Ketchup is a thixotropic fluid. Thixotropy means that the fluid viscosity decreases over time given a constant 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

From Yahoo Answers


Answers:Gravitational Force Electrical Force Magnetic Force

Question:Whats an example of a contact force, unbalanced force and a balanced force? 10 points go to the best answer.

Answers:Balanced: when you pick up a school book. The force of gravity downward on the book is equal to the force of your arm muscle pushing upward on the book. Unbalanced: when you skydive the force of gravity exceeds the force of friction from the air. Gravity force is greater which is why you fall toward the ground. Contact: simply the force when two objects are touching each exerting some form of force. Drawing a line is an example of contact force. The individual's pencil is in contact with the paper. The pencil is being pushed across the paper.

Question:what does it mean 'test AC voltage (contact testing)' & 'detects the AC power (Non-contact testing)' written in the specification of a light tester ? How can we detect the 'AC Power' with the help of light tester although AC voltage & AC power should be the same thing for a light tester because when it detects the small light bulb (fuse bulb) glows, so how can we differentiate b/w voltage & power for it. Whats contact testing & whats non-contact testing and how can we conduct it ? thanks a lot

Answers:it depends a lot on the make and model of the instrument there are voltage detectors, they will give an indication if a line is live or not, but will not indicate if 120V or 240V or something else here are a few models http://images.google.ca/images?hl=en&source=hp&q=volt+pen&btnG=Search+Images&gbv=2&aq=f&oq= some instruments need to connect to measure the voltage, but measure the current by the magnetic flux around a conductor. Here are some examples http://images.google.ca/images?gbv=2&hl=en&sa=1&q=clamp+power+meter&btnG=Search+images&aq=f&oq=&start=0 A

Question:To further explain this I will set up an example: A 150 pound man is shot out of a cannon at a constant speed of 100 miles per hour, as he is about to make contact with a wall he punches towards it at 10 miles per hour. With that example how much force was made if the man didn't punch towards the wall and how much force was made when the man did punch forward?

Answers:you just need to use F=m.a and make the diference between acelerations

From Youtube

Measuring non-contact centripetal force :Is it possible that physics has the centripetal force formula wrong for non-contact forces like gravity. The moon is not held to the Earth by a string, yet this is how the centripetal force is calculated. This video shows a clever experiment using only household items and legos to measure the the centripedal force when a non-contact force of magnetism is used to measure the centripedal force. The initial (but yet unproven) result was that the centripedal force formula that is normally used is wrong and may require new physics to explain. These are only preliminary results from a single trial. More accurate experiments will need to be done to confirm this radical finding, but it opens the door to new avenues of investigation and possibly a new way of understanding how gravity and the centripedal force interact.

Meaning Of Force :Check us out at www.tutorvista.com A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force. Forces only exist as a result of an interaction. For simplicity sake, all forces (interactions) between objects can be placed into two broad categories: contact forces, and forces resulting from action-at-a-distance Contact forces are those types of forces which result when the two interacting objects are perceived to be physically contacting each other. Examples of contact forces include frictional forces, tensional forces, normal forces, air resistance forces, and applied forces. Action-at-a-distance forces are those types of forces which result even when the two interacting objects are not in physical contact with each other, yet are able to exert a push or pull despite their physical separation. Examples of action-at-a-distance forces include gravitational forces. For example, the sun and planets exert a gravitational pull on each other despite their large spatial separation. Even when your feet leave the earth and you are no longer in physical contact with the earth, there is a gravitational pull between you and the Earth. Electric forces are action-at-a-distance forces. For example, the protons in the nucleus of an atom and the electrons outside the nucleus ...