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### Student Question

I do not understand what work is in physics?

Physics ## Explanations (1)

• Explanation from Alloprof  Explanation from Alloprof

This Explanation was submitted by a member of the Alloprof team.

Work is the energy associated with a certain movement. Work is measured when a force moves an object over a certain distance.

Work is a scalar (number), even if it is found by calculating the scalar product of two vectors (numbers with a direction). This statement may seem paradoxical, but it actually makes a lot of sense. For example, when you lift an object, your arm exerts a force on the object and lifts it a certain distance. On the other hand, the energy (the work) that it will take from you can be measured with a scalar (without direction).

Work is calculated with the following formula:

$$W = F • ∆x$$

Legend:

• W: work (J)

• F: force applied to an object (N)

• ∆x: distance of displacement of the object (m)

One can also calculate work by using the size of the applied force and displacement vectors, as well as the smallest angle between the two vectors:

$$W = ||F||•||∆x||•cos(\theta)$$

where θ represents the smallest angle between F and ∆x.

There are two special cases when calculating work:

• when the angle between the two vectors is 0 °, cos (θ) = 1, thus, work is equal to the product of the size of the two vectors.

• when the angle between the two vectors is 90 °, cos (θ) = 0, therefore, work is equal to 0. This corresponds, for example, to pressing on an object from above to make it move left and right.

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