Question

Why In work formula cosine is used? Why not sine or any other?

W = f x S cos Ф

Answer 1

any scalar product of dot product of 2 vector quantities have costheta in its formula.

Ex:A vector.B vector=ABcostheta.

in work done we take that component of force which is along displacement,i.e.,f costheta

acco to definition.

Answer 2

Answer:

First of all force is a vector quantity and displacement is also a vector quantity . Now we must understand the concept of multiplication of vectors . If we multiply two vectors $\vec{A}$ and $\vec{B}$ , then the product formed will be $cos |AB|$ . The amount of work done is the product of force and displacement and hence the formula :

$W=FScos\theta$ where W is the work done , F is the force and the displacement S takes place at an angle of $\theta$ .

Explanation:

Question is why is force a vector quantity ? Suppose I say that I am applying a force on a book lying at rest ( with respect to the table ) . Now the question you would ask me is that "where are you applying the force ?" if I ask you to find the direction of displacement .So force requires both magnitude and direction and hence is a vector quantity .

On the other hand displacement is another vector quantity as direction of displacement essentially matters . So the multiplication of vectors give cos theta × F×S which is according to the Dot Product Law of Vectors .