Work

Everything in Physics was created just to explain the phenomenon in real life. Anybody can explain it any manner. But the explanation that satisfies most of the people will be considered as the good one.

          Dot product and cross product is one of them. It is used to be taken in such way that it already exists in Nature.

It is used to define the work done by a force with dot product and the torque of a rotating object using cross product.

  

But the most essential thing that is to be noted is that,

“Work is not defined from the dot product but the dot product only was defined from Work and vice versa the Torque”.

First we will give a look to “What is meant by Work”.

Work:

When an object is moved by an external force up to a distance “d”, some kind of change is happening in the motion of the body. The change can be described the change in the velocity of that object. But to measure this change, we need to make a relation of measurable quantities with this change.

It was noticed that, “the Change is high when the force acting on the object is high”

It can be written simply as

The change is proportional to the Net external force applied on the object.

Second, it can be observed that the change is high when the displacement is high. Here displacement refers to the displacement during the force acting on that object.

So,

The change is proportional to the displacement during the force on the object.

Now, to avoid these long statements Scientists made a very small statement using specific words,

The change is described by the word – W - Work [Energy]

Work and Energy are not different. They are distinguished only by the way we look at it.

And the force acting on the body is represented by “F” and the displacement during this force is “d”

W                α                Fext * d

Taking out the proportional constant to be one   [ask Why?]   

                   W                =                Fext * d

·       In this first equation, there is no vector symbol or dot product or cross product.

The role of direction comes into play only when you deal with multiple things.

Note: The proportionality constant comes when you deal with Gravitation is different from the proportionality constant comes here in the definition of Work and the Newton’s first law.