In physics, mechanical work is the amount of energy transferred by a force. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός In Physics, a force is whatever can cause an object with Mass to Accelerate. Like energy, it is a scalar quantity, with SI units of joules. In Physics, a scalar is a simple Physical quantity that is not changed by Coordinate system rotations or translations (in Newtonian mechanics or The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity The term work was first coined in the 1830s by the French mathematician Gaspard-Gustave Coriolis. Gaspard-Gustave de Coriolis or Gustave Coriolis (21 May 1792 – 19 September 1843 was a French Mathematician, Mechanical engineer and [1]
According to the work-energy theorem if an external force acts upon an object, causing its kinetic energy to change from Ek1 to Ek2, then the mechanical work (W) is given by:[2]
where m is the mass of the object and v is the object's speed. The kinetic energy of an object is the extra Energy which it possesses due to its motion Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object Speed is the rate of motion, or equivalently the rate of change in position often expressed as Distance d traveled per unit of
When the force is in the same direction as the displacement, the mechanical work can be calculated from the scalar multiplication of the applied force (F) and the displacement (d) of the object. In Physics, a force is whatever can cause an object with Mass to Accelerate. This is given by:
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Introduction
Work can be zero even when there is a force. The centripetal force in uniform circular motion, for example, does zero work because the kinetic energy of the moving object doesn't change. The centripetal force is the external force required to make a body follow a curved path In Physics, circular motion is Rotation along a Circle: a circular path or a circular Orbit. The kinetic energy of an object is the extra Energy which it possesses due to its motion Likewise, when a book sits on a table, the table does no work on the book, because no energy is transferred into or out of the book.
Heat conduction is not considered to be a form of work, since there is no macroscopically measurable force, only microscopic forces occurring in atomic collisions.
Units
The SI unit of work is the joule (J), which is defined as the work done by a force of one newton acting over a distance of one meter. In Thermodynamics, work is the quantity of Energy transferred from one system to another without an accompanying transfer of Entropy. The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity The newton (symbol N) is the SI derived unit of Force, named after Isaac Newton in recognition of his work on Classical The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International This definition is based on Sadi Carnot's 1824 definition of work as "weight lifted through a height", which is based on the fact that early steam engines were principally used to lift buckets of water, through a gravitational height, out of flooded ore mines. Nicolas Léonard Sadi Carnot (1 June 1796 &ndash 24 August 1832 was a French Physicist and Military engineer who in his 1824 Reflections The dimensionally equivalent newton-meter (N·m) is sometimes used instead; however, it is also sometimes reserved for torque to distinguish its units from work or energy. Newton metre is the unit of moment ( Torque) in the SI system A torque (τ in Physics, also called a moment (of force is a pseudo- vector that measures the tendency of a force to rotate an object about
Non-SI units of work include the erg, the foot-pound, the foot-poundal, and the liter-atmosphere. An erg is the unit of Energy and Mechanical work in the centimetre-gram-second (CGS system of units symbol "erg" The foot-pound force, or simply foot-pound (symbol ft·lbf or ft·lb) is a unit of work or Energy (a scalar The Foot-poundal is a non- SI unit of Energy or work. The foot-poundal is the amount of energy expended when a Force of one Poundal
Mathematical calculation
Force and displacement
Force and displacement are both vector quantities and they are combined using the dot product to evaluate the mechanical work, a scalar quantity:
(1)
where φ is the angle between the force and the displacement vector. In Mathematics, the dot product, also known as the scalar product, is an operation which takes two vectors over the Real numbers R
In order for this formula to be valid, the force and angle must remain constant. The object's path must always remain on a single, straight line, though it may change directions while moving along the line.
In situations where the force changes over time, or the path deviates from a straight line, equation (1) is not generally applicable although it is possible to divide the motion into small steps, such that the force and motion are well approximated as being constant for each step, and then to express the overall work as the sum over these steps. For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of
The general definition of mechanical work is given by the following line integral:
(2)
where:
- C is the path or curve traversed by the object;
- F is the force vector;
- s is the position vector. In Mathematics, a line integral (sometimes called a path integral or curve integral) is an Integral where the function to be integrated In Mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object In Physics, a force is whatever can cause an object with Mass to Accelerate. A position, location or radius vector is a vector which represents the position of an object in space in relation to an arbitrary reference
The expression δW=F·ds is an inexact differential which means that the calculation of WC is path-dependent and cannot be differentiated to give F·ds. In Thermodynamics, an inexact differential or imperfect differential is any quantity particularly Heat Q and work W that are not State
Equation (2) explains how a non-zero force can do zero work. The simplest case is where the force is always perpendicular to the direction of motion, making the integrand always zero. The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space This is what happens during circular motion. However, even if the integrand sometimes takes nonzero values, it can still integrate to zero if it is sometimes negative and sometimes positive.
The possibility of a nonzero force doing zero work illustrates the difference between work and a related quantity, impulse, which is the integral of force over time. In Classical mechanics, an impulse is defined as the Integral of a Force with respect to Time: \mathbf{I} = \int \mathbf{F}\ Impulse measures change in a body's momentum, a vector quantity sensitive to direction, whereas work considers only the magnitude of the velocity. In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product For instance, as an object in uniform circular motion traverses half of a revolution, its centripetal force does no work, but it transfers a nonzero impulse.
Mechanical energy
The mechanical energy of a body is that part of its total energy which is subject to change by mechanical work. In Physics, mechanical energy describes the Potential energy and Kinetic energy present in the components of a mechanical system. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός It includes kinetic energy and potential energy. The kinetic energy of an object is the extra Energy which it possesses due to its motion Potential energy can be thought of as Energy stored within a physical system Some notable forms of energy that it does not include are thermal energy (which can be increased by frictional work, but not easily decreased) and rest energy (which is constant as long as the rest mass remains the same). Thermal energy is the sum of the sensible energy and latent energy. Friction is the Force resisting the relative motion of two Surfaces in contact or a surface in contact with a fluid (e The rest energy E or rest mass-energy of a particle is its energy when it is at rest relative to a given Inertial reference frame.
If an external force F acts upon a body, causing its kinetic energy to change from Ek1 to Ek2, then:[3]
Thus we have derived the result, that the mechanical work done by an external force acting upon a body is proportional to the difference in the squares of the speeds. The kinetic energy of an object is the extra Energy which it possesses due to its motion (It should be observed that the last term in the equation above is Δv2 rather than (Δv)2. )
The principle of conservation of mechanical energy states that, if a system is subject only to conservative forces (e. A conservative force is defined as a Force with the following property when an object moves from one location to another the force changes the Potential energy of g. only to a gravitational force), or if the sum of the work of all the other forces is zero, its total mechanical energy remains constant. Newton 's law of universal Gravitation is a physical law describing the gravitational attraction between bodies with mass
For instance, if an object with constant mass is in free fall, the total energy of position 1 will equal that of position 2.
where
- Ek is the kinetic energy, and
- Ep is the potential energy. The kinetic energy of an object is the extra Energy which it possesses due to its motion Potential energy can be thought of as Energy stored within a physical system
The external work will usually be done by the friction force between the system on the motion or the internal-non conservative force in the system or loss of energy due to heat.
References
- ^ Jammer, Max (1957). Concepts of Force. Dover Publications, Inc. . ISBN 0-486-40689-X.
- ^ Tipler (1991), page 138.
- ^ Zitzewitz,Elliott, Haase, Harper, Herzog, Nelson, Nelson, Schuler, Zorn (2005). Physics: Principles and Problems. McGraw-Hill Glencoe, The McGraw-Hill Companies, Inc. . ISBN 0-07-845813-7.
Bibliography
- Serway, Raymond A. ; Jewett, John W. (2004). Physics for Scientists and Engineers, 6th ed. , Brooks/Cole. ISBN 0-534-40842-7.
- Tipler, Paul (1991). Physics for Scientists and Engineers: Mechanics, 3rd ed. , extended version, W. H. Freeman. ISBN 0-87901-432-6.
External links
- Work - a chapter from an online textbook
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