Work (physics)

In science, work is a way to describe how energy moves when a force pushes or pulls something. Imagine you push a toy car across the floor. The force you use and how far the car moves are both important. If you push the car forward, your force does positive work. If something, like friction, works against the car’s motion, it does negative work.

Work happens when a force acts on an object and the object moves. For example, when a ball falls to the ground, gravity does positive work on it. When you throw a ball up, gravity does negative work because it acts opposite to the ball’s motion.

Work is measured in joules, the same unit we use for energy. It helps us understand how forces change the energy of objects, making it a key idea in physics.

History

The ancient Greeks studied simple machines like balances but did not understand dynamics or the idea of work. During the Renaissance, scientists began to explore how these machines could lift heavy loads, leading to the new idea of mechanical work. Italian scientist Galileo Galilei explained in 1600 that simple machines do not create energy; they only change how it is used.

Even before the word "work" was used in science, people had similar ideas. French philosopher René Descartes noted that lifting a heavy object a short distance uses the same effort as lifting a lighter object a longer distance. Later, German philosopher Gottfried Leibniz showed that lifting a lighter object higher up needs the same effort as lifting a heavier object a shorter distance.

The words "work" and "mechanical work" were first used in the 1820s by French scientists Gaspard-Gustave Coriolis and Jean-Victor Poncelet. They were studying how machines, like steam engines, could move and power things.

Units

The SI unit of work is the joule (J), named after English physicist James Prescott Joule. It is defined as the work done when a force of 1 newton moves an object 1 metre in the direction of the force.

Other units for work include the foot-pound from the English system, the erg, the foot-poundal, the kilowatt hour, and the horsepower-hour. Sometimes units usually used for heat or energy, like the therm, BTU, and calorie, are also used to measure work.

Work and energy

When a steady force pushes or pulls an object and the object moves in the same direction, we say that work is done. The amount of work depends on how strong the force is and how far the object moves. For example, if a force of 10 newtons moves an object 2 meters, the work done is 20 joules. This is similar to the effort needed to lift a small object against gravity.

Work is closely linked to energy. Both use the same unit of measurement, joules. When work is done on an object, energy is transferred to that object. If the work adds energy, the object moves faster. If the work takes energy away, the object slows down. This shows that work changes the energy of an object, just like moving things around can change how fast they go.

Constraint forces

Constraint forces control how an object moves, keeping it within certain limits. For example, when an object is on a slope, it can only move along the slope and not straight up or down. These forces prevent movement in certain directions, so they do not add or take away energy from the object.

In simple machines like pulleys or when a ball moves in a circle, certain forces do no work because they are perpendicular to the direction of motion. For example, the force from a string keeping a ball moving in a circle does not change the ball’s speed, only its direction. Similarly, magnetic forces can change the direction of a moving charged particle but do not change its speed.

Mathematical calculation

Work is the energy moved to or from an object when a force is used to make it move. If the force is in the same direction as the movement, it does positive work.

When we look at how fast work is done, we use a measure called power. Power is how much work is done each second and is measured in watts. It depends on the strength of the force and how fast the object is moving.

For simple cases, where the force is constant and in the same direction as the movement, work is just the force multiplied by the distance moved. But when forces change or paths curve, we need more advanced math to find the work done.

Work and potential energy

Work is a way to move energy from one place to another using force. When you push something and it moves, you are doing work. The amount of work depends on how strong the force is and how far the object moves in the direction of the force.

If the force stays the same and moves in a straight line, the work is simply the force multiplied by the distance. Forces can also change depending on where you are, like gravity, which gets weaker the farther you are from Earth. Sometimes the work done only depends on the start and end points, not the path taken. This is true for forces like gravity and springs, which have something called potential energy connected to them.

Work–energy principle

The work–energy principle says that the work done on an object by all the forces acting on it equals the change in the object's kinetic energy. This means that if you push an object and it moves, the work you do changes how fast the object is moving.

For example, if you push a toy car across the floor, the work you do makes the car go faster. If you stop pushing, the car might slow down because of friction, and the work done by friction changes the car's kinetic energy.

This idea helps us understand how forces affect motion in many situations.

Work of forces acting on a rigid body

The work done by forces on a solid object can be figured out using the total force and turning force, called torque, at one point on the object. Imagine several forces pushing different parts of the object.

We can find the tiny bit of work each force does over a tiny move by using the speed of that point and the time it takes. Adding up all these tiny bits of work tells us the total work, which ends up depending only on the total force and total torque at a chosen point on the object.

This shows that we don’t need to know how each force moves separately — just the overall push and turn at one spot tells us all about the work done.