The Definition of Work in Physics

Newton's cradle (Digital)
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In physics, work is defined as a force causing the movement—or displacement—of an object. In the case of a constant force, work is the scalar product of the force acting on an object and the displacement caused by that force. Though both force and displacement are vector quantities, work has no direction due to the nature of a scalar product (or dot product) in vector mathematics. This definition is consistent with the proper definition because a constant force integrates to merely the product of the force and distance.

Read on to learn some real-life examples of work as well as how to calculate the amount of work being performed.

Examples of Work

There are many examples of work in everyday life. The Physics Classroom notes a few: a horse pulling a plow through the field; a father pushing a grocery cart down the aisle of a grocery store; a student lifting a backpack full of books upon her shoulder; a weightlifter lifting a barbell above his head; and an Olympian launching the shot-put.

In general, for work to occur, a force has to be exerted on an object causing it to move. So, a frustrated person pushing against a wall, only to exhaust himself, is not doing any work because the wall does not move. But, a book falling off a table and hitting the ground would be considered work, at least in terms of physics, because a force (gravity) acts on the book causing it to be displaced in a downward direction.

What's Not Work

Interestingly, a waiter carrying a tray high above his head, supported by one arm, as he walks at a steady pace across a room, might think he's working hard.

(He might even be perspiring.) But, by definition, he is not doing any work. True, the waiter is using force to push the tray above his head, and also true, the tray is moving across the room as the waiter walks. But, the force—the waiter's lifting of the tray—does not cause the tray to move. "To cause a displacement, there must be a component of force in the direction of the displacement," notes The Physics Classroom.

Calculating Work

The basic calculation of work is actually quite simple:

W = Fd

Here, "W" stands for work, "F" is the force, and "d" represents displacement (or the distance the object travels). Physics for Kids gives this example problem:

A baseball player throws a ball with a force of 10 Newtons. The ball travels 20 meters. What is the total work?

To solve it, you first need to know that a Newton is defined as the force necessary to provide a mass of 1 kilogram (2.2 pounds) with an acceleration of 1 meter (1.1 yards) per second. A Newton  is generally abbreviated as "N." So, use the formula:

W = Fd

Thus:

W = 10 N * 20 meters (where the symbol "*" represents times)

So:

Work = 200 joules

joule, a term used in physics, is equal to the kinetic energy of 1 kilogram moving at 1 meter per second.

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Jones, Andrew Zimmerman. "The Definition of Work in Physics." ThoughtCo, Nov. 26, 2017, thoughtco.com/work-2699023. Jones, Andrew Zimmerman. (2017, November 26). The Definition of Work in Physics. Retrieved from https://www.thoughtco.com/work-2699023 Jones, Andrew Zimmerman. "The Definition of Work in Physics." ThoughtCo. https://www.thoughtco.com/work-2699023 (accessed December 14, 2017).