Work in physics. Force and distance

09/05/2026

The online simulations of work in physics on this page will allow you to discover in a practical way this important concept of classical mechanics, also called mechanical work or simply work. We will discover what is work in physics, what is its calculation formula, the relationship between work and energy and finally its importance and applications.

This Thematic Unit is part of our Physics collection

Conservative Force

Force that allows recovering all work performed (such as gravity), as its labor does not depend on the path.

Dissipative Force

Force that transforms work into non-recoverable energy, usually heat (such as friction), depending on the path.

Joule

Unit of energy and work equivalent to the work performed by a force of one newton acting over a distance of one meter.

Mechanical Work

Scalar quantity resulting from force by displacement and the cosine of the angle between them, measured in joules (J).

Power

Rate at which work is performed, defined as work per unit of time and measured in watts (W).

Watt

Unit of power representing the transfer or consumption of one joule of energy per every second of time.

Concept of work in physics

Work in phiscis is a fundamental concept that refers to the transfer of energy from one object to another by applying a force over a distance.

Calculation of work in physics. Force and distance

Work is calculated by multiplying the magnitude of the applied force by the distance over which it is applied. Mathematically, work (W) is defined as the scalar product of the force (F) applied and the distance (d) made by the object in the direction of the force.

The formula for work in physics is as follows:

W = F * d * cos(θ)

where θ is the angle between the force and displacement vectors.

Therefore, work is a scalar quantity that, depending on the value of the angle θ, can be positive or negative. Its unit of measurement in the International System is the joule (J).

Work and energy

Work and energy are deeply interrelated in physics, since work done on an object causes a change in its energy. When a force is applied over a distance and work is done, the energy of the object can be transformed, either by increasing its kinetic energy, its potential energy, or both. This principle highlights how work acts as the link that allows energy to be transferred between systems, making it an essential concept for understanding conservation laws and dynamic processes in nature.

Conservative Force

Force that allows recovering all work performed (such as gravity), as its labor does not depend on the path.

Dissipative Force

Force that transforms work into non-recoverable energy, usually heat (such as friction), depending on the path.

Joule

Unit of energy and work equivalent to the work performed by a force of one newton acting over a distance of one meter.

Mechanical Work

Scalar quantity resulting from force by displacement and the cosine of the angle between them, measured in joules (J).

Power

Rate at which work is performed, defined as work per unit of time and measured in watts (W).

Watt

Unit of power representing the transfer or consumption of one joule of energy per every second of time.

Explore the exciting STEM world with our free, online, simulations and accompanying companion courses! With them you’ll be able to experience and learn hands-on. Take this opportunity to immerse yourself in virtual experiences while advancing your education – awaken your scientific curiosity and discover all that the STEM world has to offer!

Work of a force

In the first of our simulations of work in physics, we examine the work done by a force applied on a block. Pull the block and observe on the graph the work done as it moves.

Lift a mass

Lift a mass by pulling it. Observe the difference in work done when it is lifted gently and when it is lifted roughly, can you explain?

Giants of science

“If I have seen further, it is by standing on the shoulders of giants”

Isaac Newton

Léon Foucault

1819

–

1868

Léon Foucault demonstrated Earth’s rotation with his famous pendulum and measured the speed of light with great precision, revolutionizing experimental optics

“The pendulum does not lie: the Earth moves beneath our feet”

Leonhard Euler

1707

–

1783

Euler developed much of modern mathematical notation and made key contributions to analysis, topology, mechanics, and graph theory

“Nothing takes place in the universe without mathematics expressing it”

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Gaspard-Gustave de Coriolis

1792

–

1843

Gaspard-Gustave de Coriolis formulated the effect that bears his name, explaining the deflection of bodies on Earth’s rotation and providing key foundations for mechanics.

“Motion is not only trajectory, it is also invisible influence”

Archimedes

287 a.C.

–

212 a.C.

Archimedes established fundamental principles of mechanics and hydrostatics, including the famous Archimedes’ principle of buoyancy in fluids

“Give me a place to stand, and I will move the world”

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Test your knowledge

How is work defined in physics, and why is this concept essential for understanding energy transfer between systems?

In physics, work is defined as the product of a force applied to an object and the displacement that occurs in the direction of that force. This definition is fundamental because it links motion with energy: whenever a force causes an object to move, energy is being transferred into or out of that object. For example, pushing a block so that it slides across a surface increases its mechanical energy, while resisting its motion removes energy from it. The concept of work allows us to quantify these exchanges precisely and to understand how physical systems evolve. It acts as a bridge between dynamics (forces and motion) and energetics (how energy changes within a system), making it indispensable for analyzing everything from simple mechanical interactions to complex physical processes.

Why does work depend on the angle between the force and the displacement, and how does this influence the physical interpretation of the process?

Work only considers the component of the force that acts in the same direction as the displacement. This is why the cosine of the angle between force and displacement appears in the formula. When the force is aligned with the motion, the work is maximized; when the force is perpendicular, the work is zero because it does not contribute to moving the object in that direction. This angular dependence helps distinguish between forces that genuinely produce motion and those that merely modify other aspects of the system, such as the normal force or internal stresses. It also explains why some forces perform negative work, like friction, which opposes motion and removes energy from the system. Understanding this geometric interpretation is crucial for analyzing real situations such as pulling objects at an angle, braking, or moving along inclined surfaces.

Why is it that sometimes I push something and physics says I did “no work”? Does it really make sense that it only counts if it moves?

Yes, it makes complete sense from a physics standpoint. Work requires displacement. If you push a wall with all your strength but it doesn’t move, you haven’t transferred mechanical energy to it, so no physical work has been done on the wall. Your fatigue comes from internal processes in your body, not from work performed on the object. Physics focuses strictly on whether energy is transferred to the external system, and without motion, that transfer doesn’t occur.

What happens if a force acts opposite to the direction of motion? How come it can do “negative work”?

When a force acts against the direction of motion, it removes energy from the system instead of adding it. That’s why we say it performs negative work. Friction is the classic example: as an object slides, friction acts in the opposite direction and reduces its kinetic energy. This negative work explains why objects slow down and eventually stop unless another force supplies additional energy to counteract the loss.

Does it make sense that applying a huge force over a tiny distance results in very little work? Why doesn’t the large force dominate?

It makes perfect sense. Work depends on both force and displacement. A very large force applied over a very small distance transfers only a small amount of energy. This is why lifting a heavy object just a few centimeters requires far less work than lifting it a full meter, even though the force needed is the same. The key factor is how much energy is actually transferred, and that depends on the product of force and distance, not on force alone.