Why is the work a scalar quantity?

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ishpiro eNotes educator| Certified Educator

A scalar quantity is a quantity that can be measured by one number. This is in contrast to a vector quantity, that has to be represented by two, or more, numbers. For example, velocity is a vector quantity because it indicates how fast an object is moving, and in what direction.

Force is also a vector quantity, because it represents the strength of the push or pull, and also the direction of that push or pull. Work, however, is a quantity that indicates the result of the force's action: it combines the force with displacement that occurred in the direction of that force. Mathematically, it is expressed as follows:


This is called a scalar product of the two vectors: the force vector and the displacement vector. It is a scalar because the result of it is just one number, calculated as follows:

`W =|vecF||Deltavecx|*cos(theta).`

So, work is the product of the magnitudes of the force and the displacement, and the cosine of the angle between them (`theta` ).

Work can also be thought of as a change in the kinetic energy of and object. The kinetic energy is

`K = 1/2mv^2` , where m is the mass and v is the speed of the object. Since mass and speed are scalar quantities (speed is a magnitude of velocity, and this a scalar), kinetic energy is also a scalar quantity, so the work, which equals the change in kinetic energy, is also a scalar quantity.


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