Name: work in force and motion
Uploaded: 2023-09-22T11:49:36.000Z
Duration: 1 min 14 s
Channel: JoVE

Il lavoro si ottiene quando una forza che agisce su un oggetto lo sposta. È uguale al prodotto della componente scalare della forza lungo la direzione di spostamento.
Matematicamente, il lavoro può essere dato come il prodotto scalare della forza applicata e dello spostamento dell'oggetto.
L'unità di lavoro SI è il joule. Un joule è il lavoro svolto quando una forza di un newton sposta un oggetto di un metro.
Poiché il lavoro è una grandezza scalare, la sua grandezza può essere positiva, negativa o zero a seconda della direzione della forza relativa allo spostamento.

Considera l'esempio di una gru che solleva un carico verso l'alto. Qui, i vettori di forza applicata e di spostamento sono allineati nella stessa direzione, quindi il lavoro svolto è positivo.

In un altro esempio, quando i freni vengono applicati a un'auto in movimento, la forza frenante agisce nella direzione opposta al movimento dell'auto. Qui, il lavoro svolto è negativo.

Una puleggia senza attrito che solleva un carico attraverso una corda inestensibile senza massa non fa alcun lavoro poiché la forza e lo spostamento sono perpendicolari.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica: Statica. Quattordicesima edizione, New Jersey: Pearson. Sezione 11.1, pp. 581-582.</li>
	<li>Meriam, J.L., Kraige, L.G. e Bolton, J.N. (2016). Meccanica ingegneristica: statica e dinamica. Ottava edizione, Singapore: John Wiley & Sons. Sezione 7.2, pp. 392-393.</li>
	<li>Birra, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. e Self, B.P. (2016). Meccanica vettoriale per ingegneri. Undicesima edizione, New York: McGraw-Hill Education. Sezione 10.1A pp. 575.</li>
</ol>

lavoro

Il lavoro è un concetto fondamentale dell'ingegneria meccanica ed ha molte applicazioni. Comprendere come viene calcolato il lavoro e i diversi tipi di lavoro, può aiutarci a capire meglio i processi fisici e fornire spunti su problemi complessi.

Il lavoro viene definito come il risultato di una forza che agisce su un oggetto, causandone lo spostamento lungo la linea di azione della forza. Viene anche definito come il processo di trasferimento di energia attraverso l'applicazione di una forza su un oggetto, con conseguente spostamento. Questo trasferimento di energia è responsabile del cambiamento nel movimento o della posizione dell'oggetto. Il lavoro può essere espresso come il prodotto della forza per la componente di spostamento nella stessa direzione, oppure può essere espresso come il prodotto scalare della forza applicata e dello spostamento dell'oggetto. Nel sistema internazionale il joule è considerato la sua unità - questo è equivalente ad applicare una newton di forza su un metro di spostamento.

Il tipo di lavoro eseguito su un oggetto dipende dalla direzione della forza rispetto allo spostamento. Se la forza applicata e lo spostamento sono paralleli tra loro, il lavoro fatto è positivo e se sono antiparalleli, il lavoro fatto è negativo. Quando la forza applicata e lo spostamento sono perpendicolari tra loro, il lavoro fatto è zero. Un esempio di lavoro positivo è quando una gru solleva un carico pesante - esercitando una forza verso l'alto sul carico, si muove rispetto al livello del suolo. Il lavoro negativo si verifica, ad esempio, quando vengono utilizzati i freni su una macchina in movimento - le ruote esercitano una forza contraria al suo movimento, con conseguente lavoro negativo su di essa.

Alcune forze, come quelle che agiscono su punti fissi o perpendicolari allo spostamento, non svolgono alcun lavoro. Esempi includono la reazione in un perno privo di attrito quando il corpo sospeso ruota intorno ad esso, la forza di reazione che agisce su un corpo che si muove su una superficie priva di attrito, ecc. Viceversa, le forze che compiono lavoro includono il peso di un corpo e la forza di attrito che agisce su un corpo che si muove su una superficie ruvida.

In alcuni casi, la somma del lavoro eseguito da multiple forze risulta essere zero. Ad esempio, due corpi rigidi connessi da un perno privo di attrito, richiedono forze uguali ma opposte per il movimento, quindi il loro lavoro combinato è zero. Allo stesso modo, due blocchi connessi da un cordino estensibile hanno forze di tensione di uguale grandezza ma segni opposti, risultando in un lavoro nullo.

Complessivamente, comprendere quali forze producono lavoro e come calcolare il lavoro, può fornire spunti utili su problemi fisici complessi e consentirci di gestire efficacemente questi processi per ottenere i risultati desiderati.

Lavoro

Il lavoro è un concetto fondamentale dell'ingegneria meccanica e ha molte applicazioni. Capire come si calcola il lavoro e i diversi tipi di lavoro...

Education

Didattica

JoVE Core

Mechanical Engineering

Ingegneria Meccanica

Unit 1

Unità 1

Virtual Work

Lavoro virtuale

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

Work

work in force and motion

Work connects force, motion, and energy in mechanics. It happens when a force acts on an object and the object moves along the line of action of that force. Work can also be described as energy transfer caused by applying a force, which leads to a change in the object’s motion or position.

Work is calculated as the force multiplied by the part of the displacement in the same direction as the force. It can also be written as the dot product of the applied force and the object’s displacement. In the SI system, the unit of work is the joule. One joule is equal to one newton of force acting over one meter of displacement.

The direction of the force compared with the displacement tells us the type of work done. When the force and displacement are parallel, the work is positive. When they are anti-parallel, the work is negative. When the force and displacement are perpendicular, the work is zero.

A crane lifting a heavy load is an example of positive work. The crane applies an upward force, and the load moves upward. Brakes on a moving car show negative work. The wheels exert a force that opposes motion, so work is done against the car’s movement.

Some forces do no work. This includes forces acting at fixed points or forces perpendicular to displacement. Examples include the reaction at a frictionless pin when a body rotates about it, and the reaction force on a body moving on a frictionless surface. Forces that do work include the weight of a body and friction acting on a body moving on a rough surface.

In some systems, the total work done by multiple forces is zero. Two rigid bodies connected by a frictionless pin need equal and opposite forces for motion, so their combined work is zero. The same idea applies to two blocks connected by an extensible cord, where the tension forces have equal magnitude but opposite signs. Knowing which forces produce work helps explain physical processes and solve mechanical problems.

Work in Force and Motion

work

Work connects force, motion, and energy in mechanics. It happens when a force acts on an object and the object moves along the line of action of that force. Work can also be described as energy transfer caused by applying a force, which leads to a change in the object’s motion or position. Work is calculated as the force multiplied by the part of the displacement in the same direction as the force. It can also be written as the dot product of the applied force and the object’s displacement. In...

work of a couple moment

Couple Moment Work in Rotation

Mechanical engineering studies motion, energy, and force, and it uses the idea of a couple moment to describe how two equal and opposite forces act on a rigid body. A couple moment is created when those forces act at two points on the body that are separated by a distance. When a rigid body moves because of a couple, its displacement can be split into two parts. First, the two points move by the same amount to their final positions. Then the body rotates about one of those points. During the...

virtual work

Virtual Work in Force Equilibrium

Virtual work is a mechanics principle used to check equilibrium with imaginary motion. If a body is in static or dynamic equilibrium, the total virtual work from external forces and couple moments must be zero for any virtual displacement. A virtual displacement is an imagined small movement. It can be a shift or a rotation. The virtual work done by a force equals the force dotted with the virtual displacement in the force’s direction. For a couple moment, virtual rotational work is found by...

virtual work for a system of connected rigid bodies

virtual-work-for-a-system-of-connected-rigid-bodies

Finding Forces with Virtual Work in Linked Bodies

Virtual work helps find forces in a system of connected rigid bodies. It is a useful method when several links move together and the system is in equilibrium. In that case, the total virtual work is zero. To analyze the system, start with a free-body diagram. Use one independent coordinate to describe the link configuration. Then mark the deflected position that comes from a positive virtual displacement. This makes the small change in position clear before any calculations begin. Next,...

principle of virtual work: problem solving

principle-of-virtual-work-problem-solving

Virtual Work for Finding Unknown Forces

The principle of virtual work helps find unknown forces and moments in equilibrium problems. It is an important idea in mechanics and engineering. The method uses a small, hypothetical motion called a virtual displacement. If the system is in equilibrium, the work done by the forces during that displacement is zero. To apply this principle, the positions of the internal and external forces must be written in terms of one common coordinate parameter. That parameter can be an angle, a distance,...

mechanical efficiency of real machines

Friction’s Role in Machine Efficiency

Mechanical efficiency shows how well a machine turns input work into output work. It is calculated as the ratio of output work to input work. An ideal machine has an efficiency of one, which means the input work equals the output work. Real machines are never perfectly ideal because some energy is lost. Friction is one of the main causes of that loss. In a toggle vise used to compress wooden blocks, the sliding block rubs against the horizontal plane and creates friction. To find the...

conservative forces

Conservative Forces and Path-Independent Work

Conservative forces are forces whose work depends only on an object’s starting and ending positions. The path between those positions does not change the amount of work done. This idea is important in mechanical engineering because it helps describe how energy moves through a system. A conservative force also conserves energy in the sense that its work is path independent. Gravity is one example. Electrostatic forces and springs modeled by Hooke’s law are also examples. A ball rolling down a...

potential energy

Gravitational and Elastic Energy Stored

Gravitational and elastic potential energy are forms of stored energy from conservative forces. A conservative force, such as gravity or an elastic force, gives a body the capacity to do work. This capacity is measured as potential energy and depends on the body’s position relative to a fixed reference point, or datum. For gravitational potential energy, the datum is the level where the energy is taken as zero. If a body is above this reference plane, its weight has positive gravitational...

potential-energy criterion for equilibrium

potential-energy-criterion-for-equilibrium

Stable Equilibrium Through Potential Energy

Potential energy helps determine when a mechanical system is stable at equilibrium. When a system is acted on by gravitational and elastic forces, its total potential function is the algebraic sum of gravitational potential energy and elastic potential energy. If the system is already in equilibrium and is given a small displacement, the work done on the system equals the negative of the change in potential energy between the starting and ending positions. For a virtual displacement, which is...

stability of equilibrium configuration

Types of Equilibrium in Mechanical Systems

Types of equilibrium in mechanical systems are stable, neutral, and unstable. These three cases help explain how a structure or object responds when it is pushed slightly away from balance. They are important for predicting whether a system will return to its original position, stay where it is, or move farther away. Stable equilibrium occurs when a system returns toward its original position after a small displacement. In this case, the potential energy is at a minimum. A cantilever beam...

one-degree-of-freedom system

Spring-Mass Motion and Energy Stability

A one-degree-of-freedom system uses a single independent variable to describe its state and behavior. In mechanical engineering, this kind of model helps explain how parts in a larger system respond to force. It also gives engineers a way to predict motion before a design is built in real life. A simple harmonic oscillator is one example of a one-degree-of-freedom system. A mass attached to a spring moves along one axis, and that position determines the system’s state. The spring force makes...

stability of equilibrium configuration: problem solving

stability-of-equilibrium-configuration-problem-solving

Equilibrium Stability Through Potential Energy

Stability of equilibrium in physics and engineering can be studied by using a system’s potential energy. An equilibrium configuration is a state where the system can remain at rest. Stability describes whether the system tends to return to that state after a small disturbance. Problem solving begins by finding the equilibrium points of the system. This is done by setting the derivative of the potential energy function equal to zero and solving for the independent variable values that satisfy...

key terms and concepts

Learn how work is calculated from force and displacement, why it can be positive, negative, or zero, and see real examples from cranes and brakes.

Work in Force and Motion | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Work in Force and Motion

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