In physics Physics is a natural science that involves the study of matter and its motion through space-time, as well as all applicable concepts, such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves, mechanical work is the amount of energy In physics, energy is a quantity that can be assigned to every particle, object, and system of objects as a consequence of the state of that particle, object or system of objects. Different forms of energy include kinetic, potential, thermal, gravitational, sound, elastic, light, and electromagnetic energy. The forms of energy are often named transferred by a force In physics, a force is any influence that causes a free body to undergo an acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform. A force has both magnitude and direction, making it a acting through a distance. Like energy, it is a scalar In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations (in relativity). (Contrast to vector.) quantity, with SI units The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science of joules The joule , named after James Prescott Joule, is the derived unit of energy in the International System of Units. It is the energy exerted by the force of one newton acting to move an object through a distance of one metre. In terms of dimensions:. The term work was first coined in 1826 by the French mathematician Gaspard-Gustave Coriolis.[1][2]

According to the work-energy theorem if an external force acts upon a rigid object, causing its kinetic energy The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude to change from Ek1 to Ek2, then the mechanical work (W) is given by:[3]

where m is the mass In physics, mass commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: Inertial mass, active gravitational mass and passive gravitational mass. In everyday usage, mass is often taken to mean weight, but in scientific use, they refer to different properties of the object and v is the object's velocity In physics, velocity is the rate of change of position. It is a vector physical quantity; both magnitude and direction are required to define it. The scalar absolute value of velocity is speed, a quantity that is measured in meters per second (m/s or ms−1) when using the SI (metric) system.

If the resultant force F on an object acts while the object is displaced a distance d, and the force and displacement act parallel to each other, the mechanical work done on the object is the product of F multiplied by d:[4]

If the force and the displacement are parallel and in the same direction, the mechanical work is positive. If the force and the displacement are parallel but in opposite directions (i.e. antiparallel), the mechanical work is negative.

However, if the force and the displacement act perpendicular to each other, zero work is done by the force:[4]

Contents

Units

Main article: work (thermodynamics) In thermodynamics, work performed by a system is the quantity of energy transferred by the system to another that is accounted for in a particular way; namely, by changes in the external generalized mechanical constraints on the system

The SI unit of work is the joule The joule , named after James Prescott Joule, is the derived unit of energy in the International System of Units. It is the energy exerted by the force of one newton acting to move an object through a distance of one metre. In terms of dimensions: (J), which is defined as the work done by a force of one newton The newton is the SI derived unit of force, named after Isaac Newton in recognition of his work on classical mechanics acting over a distance of one meter The metre , symbol m, is the base unit of length in the International System of Units (SI). Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole, its definition has been periodically refined to reflect growing knowledge of metrology. Since 1983, it is defined as the distance travelled by light in a. This definition is based on Sadi Carnot Nicolas Léonard Sadi Carnot was a French physicist and military engineer who, in his 1824 Reflections on the Motive Power of Fire, gave the first successful theoretical account of heat engines, now known as the Carnot cycle, thereby laying the foundations of the second law of thermodynamics. He is often described as the "Father of'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. The dimensionally equivalent newton-meter Newton metre is a unit of torque in the SI system. Less commonly, it is used as a unit of energy, in which case it is synonymous with the more common and standard SI unit of energy, the joule. The symbolic form is N m or N·m, and sometimes hyphenated newton-metre. One newton metre is equal to the torque resulting from a force of one newton (N·m) is sometimes used instead; however, it is also sometimes reserved for torque Torque, also called moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist to distinguish its units from work or energy.

Non-SI units of work include the erg An erg is the unit of energy and mechanical work in the centimetre-gram-second system of units, symbol "erg". Its name is derived from the Greek ergon, meaning "work", the foot-pound The foot-pound force, or simply foot-pound is a unit of work or energy (a scalar), the foot-poundal 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 acts through a distance of 1 foot along the direction of the force and is defined as 1 ft•pdl. The foot-poundal can also be expressed as the calculable energy or work done over the distance of one foot by a one pound, and the liter-atmosphere.

Heat conduction is not considered to be a form of work, since the energy is transferred into atomic vibration rather than a macroscopic displacement

Zero work

A baseball Baseball is a bat-and-ball sport played between two teams of nine players each. The goal is to score runs by hitting a thrown ball with a bat and touching a series of four bases arranged at the corners of a ninety-foot square, or diamond. Players on one team take turns hitting against the pitcher of the other team (the fielding team), which tries pitcher In baseball, the pitcher is the player who throws the baseball from the pitcher's mound toward the catcher to begin each play, with the goal of retiring a batter who attempts to either make contact with it or draw a walk. In the numbering system used to record defensive plays, the pitcher is assigned the number 1. In the National League and the does positive work on the ball by transferring energy into it.

Work can be zero even when there is a force. The centripetal force Centripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The term centripetal force comes from the Latin words centrum and petere ("tend towards", "aim at"), signifying that the force is directed in a uniform circular motion In physics, circular motion is rotation along a circle: a circular path or a circular orbit. It can be uniform, that is, with constant angular rate of rotation, or non-uniform, that is, with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. We can talk about circular, for example, does zero work since the kinetic energy The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude of the moving object doesn't change. This is because the force is always perpendicular to the motion of the object; only the component of a force parallel to the velocity vector of an object can do work on that object. Likewise when a book sits on a table, the table does no work on the book despite exerting a force equivalent to mg upwards, because no energy is transferred into or out of the book.

Mathematical calculation

Force and displacement

Force and displacement are both vector In elementary mathematics, physics, and engineering, a Euclidean vector is a geometric object that has both a magnitude (or length) and direction. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by quantities and they are combined using the dot product In mathematics, the dot product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number obtained by multiplying corresponding entries and adding up those products. The name is derived from the centered dot "·" that is often used to designate this operation; the alternative name scalar to evaluate the mechanical work, a scalar quantity:

(1)

where is the angle between the force and the displacement vector.

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 Time is "a nonspatial continuum in which events occur in apparently irreversible succession from the past through the present to the future." It is used to sequence events, to quantify the durations of events and the intervals between them, and to quantify and measure the motions of objects and other changes. Time is quantified in, 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.

The general definition of mechanical work is given by the following line integral In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve:

(2)

where:

is the path or curve In mathematics, a curve is, generally speaking, an object similar to a straight line but which is not required to be straight. Often curves in two-dimensional or three-dimensional (space curves) Euclidean space are of interest traversed by the object;
is the force In physics, a force is any influence that causes a free body to undergo an acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform. A force has both magnitude and direction, making it a vector; and
is the position vector A position, location, or radius vector is a vector which represents the position of a point P in space in relation to an arbitrary reference origin O. It is equivalent to an imaginary displacement from O to P. The concept applies to two- or three-dimensional space. The term is also used as a means of deriving displacement by the spatial comparison.

The expression is an inexact differential In thermodynamics, an inexact differential or imperfect differential is any quantity, particularly heat Q and work W, that are not state functions , in that their values depend on how the process is performed. The symbol , or δ (in the modern sense), which originated from the work of German mathematician Carl Gottfried Neumann in his 1875 which means that the calculation of is path-dependent and cannot be differentiated to give .

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. 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. Impulse measures change in a body's momentum In classical mechanics, momentum is the product of the mass and velocity of an object (p = mv). In relativistic mechanics, this quantity is multiplied by the Lorentz factor. Momentum is sometimes referred to as linear momentum to distinguish it from the related subject of angular momentum. Linear momentum is a vector quantity, since it has a, a vector quantity sensitive to direction, whereas work considers only the magnitude of the velocity. 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.

Torque and rotation

Work done by a torque Torque, also called moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist can be calculated in a similar manner. A torque applied through a revolution of , expressed in radians, does work as follows:

Frame of reference

The work done by a force acting on an object depends on the inertial frame of reference In physics, an inertial frame of reference is a frame of reference which describes time homogeneously and space homogeneously, isotropically, and in a time independent manner. This allows motion and interactions to be described without the presence of fictitious forces. Special relativity states that there are actually infinitely many such frames,, because the distance covered while applying the force does. Due to Newton's law of reciprocal actions Newton's laws of motion are three physical laws that form the basis for classical mechanics. They have been expressed in several different ways over nearly three centuries, and can be summarised as follows: there is a reaction force; it does work depending on the inertial frame of reference in an opposite way. The total work done is independent of the inertial frame of reference.

References

  1. ^ Jammer, Max (1957). Concepts of Force. Dover Publications, Inc.. ISBN The International Standard Book Number is a unique numeric commercial book identifier based upon the 9-digit Standard Book Numbering (SBN) code created by Gordon Foster, now Emeritus Professor of Statistics at Trinity College, Dublin, for the booksellers and stationers W.H. Smith and others in 1966 0-486-40689-X.
  2. ^ Sur une nouvelle dénomination et sur une nouvelle unité à introduire dans la dynamique, Académie des sciences, August 1826
  3. ^ Tipler (1991), page 138.
  4. ^ a b Resnick, Robert and Halliday, David (1966), Physics, Section 7-2 (Vol I and II, Combined edition), Wiley International Edition, Library of Congress Catalog Card No. 66-11527

Bibliography

External links

Categories: Introductory physics This category includes topics in physics that are commonly taught in middle school or high school, or may be in the curriculum for college freshmen. See also the list of basic physics topics | Mechanics Categories: Physics | Mechanical engineering | Motion | Energy in physics | Physical quantities This category identifies Physical quantities which are necessary defined quantities, measured, manipulated, generally used by Physicists, Engineers, Chemists, etc

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Q. I'm interested in problem solving, mechanics mathematics and designing new products based on criteria etc. HOWEVER working on cars or planes doesn't really appeal to me. I guess what does appeal are odd things like artificial limbs, roller coasters and the like (I don't know why, I guess they just seem more fun?) Are there any other booming large businesses that mechanical engineers OFTEN work in other than automobiles/trains/planes (transport)?
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