The transfer of energy from one object to another, especially in order to make the second object move in a certain direction. Work is equal to the amount of force multiplied by the distance over which it is applied. If a force of 10 newtons, for example, is applied over a distance of 3 meters, the work is equal to 30 newtons per meter, or 30 joules. The unit for measuring work is the same as that for energy in any system of units, since work is simply a transfer of energy. Compare energy power.
In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force strength and the distance traveled. A force is said to do positive work if when applied it has a component in the direction of the displacement of the point of application. A force does negative work if it has a component opposite to the direction of the displacement at the point of application of the force.[1]
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For example, when a ball is held above the ground and then dropped, the work done by the gravitational force on the ball as it falls is positive, and is equal to the weight of the ball (a force) multiplied by the distance to the ground (a displacement). If the ball is thrown upwards, the work done by the gravitational force is negative, and is equal to the weight multiplied by the displacement in the upwards direction.
Work is a scalar quantity,[2] so it has only magnitude and no direction. Work transfers energy from one place to another, or one form to another. The SI unit of work is the joule (J), the same unit as for energy.
The ancient Greek understanding of physics was limited to the statics of simple machines (the balance of forces), and did not include dynamics or the concept of work. During the Renaissance the dynamics of the Mechanical Powers, as the simple machines were called, began to be studied from the standpoint of how far they could lift a load, in addition to the force they could apply, leading eventually to the new concept of mechanical work. The complete dynamic theory of simple machines was worked out by Italian scientist Galileo Galilei in 1600 in Le Meccaniche (On Mechanics), in which he showed the underlying mathematical similarity of the machines as force amplifiers.[3][4] He was the first to explain that simple machines do not create energy, only transform it.[3]
Although work was not formally used until 1826, similar concepts existed before then. Early names for the same concept included moment of activity, quantity of action, latent live force, dynamic effect, efficiency, and even force.[5] In 1637, the French philosopher Ren Descartes wrote:[6]
According to the 1957 physics textbook by Max Jammer,[9] the term work was introduced in 1826 by the French mathematician Gaspard-Gustave Coriolis[10] as "weight lifted through a height", which is based on the use of early steam engines to lift buckets of water out of flooded ore mines. According to Rene Dugas, French engineer and historian, it is to Solomon of Caux "that we owe the term work in the sense that it is used in mechanics now".[11]
The SI unit of work is the joule (J), named after the 19th-century English physicist James Prescott Joule, which is defined as the work required to exert a force of one newton through a displacement of one metre.
Non-SI units of work include the newton-metre, erg, the foot-pound, the foot-poundal, the kilowatt hour, the litre-atmosphere, and the horsepower-hour. Due to work having the same physical dimension as heat, occasionally measurement units typically reserved for heat or energy content, such as therm, BTU and calorie, are used as a measuring unit.
For example, if a force of 10 newtons (F = 10 N) acts along a point that travels 2 metres (s = 2 m), then W = Fs = (10 N) (2 m) = 20 J. This is approximately the work done lifting a 1 kg object from ground level to over a person's head against the force of gravity.
Constraint forces determine the object's displacement in the system, limiting it within a range. For example, in the case of a slope plus gravity, the object is stuck to the slope and, when attached to a taut string, it cannot move in an outwards direction to make the string any 'tauter'. It eliminates all displacements in that direction, that is, the velocity in the direction of the constraint is limited to 0, so that the constraint forces do not perform work on the system.
For a mechanical system,[14] constraint forces eliminate movement in directions that characterize the constraint. Thus the virtual work done by the forces of constraint is zero, a result which is only true if friction forces are excluded.[15]
Fixed, frictionless constraint forces do not perform work on the system,[16] as the angle between the motion and the constraint forces is always 90.[16] Examples of workless constraints are: rigid interconnections between particles, sliding motion on a frictionless surface, and rolling contact without slipping.[17]
For example, in a pulley system like the Atwood machine, the internal forces on the rope and at the supporting pulley do no work on the system. Therefore, work need only be computed for the gravitational forces acting on the bodies. Another example is the centripetal force exerted inwards by a string on a ball in uniform circular motion sideways constrains the ball to circular motion restricting its movement away from the centre of the circle. This force does zero work because it is perpendicular to the velocity of the ball.
For moving objects, the quantity of work/time (power) is integrated along the trajectory of the point of application of the force. Thus, at any instant, the rate of the work done by a force (measured in joules/second, or watts) is the scalar product of the force (a vector), and the velocity vector of the point of application. This scalar product of force and velocity is known as instantaneous power. Just as velocities may be integrated over time to obtain a total distance, by the fundamental theorem of calculus, the total work along a path is similarly the time-integral of instantaneous power applied along the trajectory of the point of application.[18]
When a force component is perpendicular to the displacement of the object (such as when a body moves in a circular path under a central force), no work is done, since the cosine of 90 is zero.[13] Thus, no work can be performed by gravity on a planet with a circular orbit (this is ideal, as all orbits are slightly elliptical). Also, no work is done on a body moving circularly at a constant speed while constrained by mechanical force, such as moving at constant speed in a frictionless ideal centrifuge.
Calculating the work as "force times straight path segment" would only apply in the most simple of circumstances, as noted above. If force is changing, or if the body is moving along a curved path, possibly rotating and not necessarily rigid, then only the path of the application point of the force is relevant for the work done, and only the component of the force parallel to the application point velocity is doing work (positive work when in the same direction, and negative when in the opposite direction of the velocity). This component of force can be described by the scalar quantity called scalar tangential component (F cos(tag_hash_142), where is the angle between the force and the velocity). And then the most general definition of work can be formulated as follows:
If the force varies (e.g. compressing a spring) we need to use calculus to find the work done. If the force as a variable of x is given by F(x), then the work done by the force along the x-axis from x1 to x2 is:
This result can be understood more simply by considering the torque as arising from a force of constant magnitude F, being applied perpendicularly to a lever arm at a distance r {\displaystyle r} , as shown in the figure. This force will act through the distance along the circular arc l = s = r {\displaystyle l=s=r\phi } , so the work done is W = F s = F r . {\displaystyle W=Fs=Fr\phi .} Introduce the torque tag_hash_144 = Fr, to obtain W = F r = , {\displaystyle W=Fr\phi =\tau \phi ,} as presented above.
The scalar product of a force F and the velocity v of its point of application defines the power input to a system at an instant of time. Integration of this power over the trajectory of the point of application, C = x(t), defines the work input to the system by the force.
The work of forces acting at various points on a single rigid body can be calculated from the work of a resultant force and torque. To see this, let the forces F1, F2, ..., Fn act on the points X1, X2, ..., Xn in a rigid body.
Notice 2021-43, issued on August 10, 2021, provided transition relief by extending the 28-day deadline for employers hiring individuals who are Designated Community Residents or Qualified Summer Youth Employees who begin work on or after January 1, 2021, and before October 9, 2021, to submit a completed Form 8850 to the designated local agency (DLA) no later than November 8, 2021.
Notice 2020-78, issued on December 11, 2020, provided transition relief for employers that hired certain individuals residing in empowerment zones by extending the 28-day deadline for employers who submit a certification request for an individual who began work between January 1, 2018, and December 31, 2020.
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