Why is work scalar and composed of f and s?

Although both F and S are vectors, the variation of kinetic energy (that is, work) is always defined as the product of the distance in the F direction. Because the direction is specified by assimilation, there is no vector meaning, only a special case where the distance is opposite to the direction of the force, that is, doing negative work.

Only the positive and negative theory of work, no vector theory.

Simply put, regardless of the direction of the force, we can consider how much F makes the object move in its own direction, and the multiplication of the two is the actual work effect of the force. This effect does not care about the direction of motion, so the vector is out of the question.

Where f is regarded as a pure scalar, s is a positive or negative scalar, azimuth is not needed, and vector operation is not allowed.

But when the analysis object is single and S is unique, F can be the resultant force or the component of some factors in the S distance, which can be understood as the sum of work or some factors.

For example, if the pulling force is greater than gravity to accelerate the lifting object to do work, the total kinetic energy is the resultant force, that is, the lifting force (= pulling force-gravity) multiplied by the height or pulling force to do positive work = pulling force multiplied by the height, and gravity to do negative work = gravity multiplied by the negative height. The total kinetic energy is as above.

This is to sum up the source of work according to the source of force, and the formula of work is the same.

In addition, in mathematics, vectors are also called vectors.

There are two kinds of vector multiplication, one is point multiplication (physically called scalar product) and the other is cross multiplication (physically called vector product).

Simply put, point multiplication means that as long as the quantity is multiplied, the definition of work makes the direction of distance and force consistent, so it is point multiplication, and at the same time it does not emphasize the direction of force itself, so both of them are scalars of quantity operation.

An example of the cross product is the moment: the product of the force and the distance from the direction perpendicular to the force to the fulcrum.

Obviously, because it is vertical, it belongs to cross multiplication, that is, because the distance between the stressed point and the fulcrum is not perpendicular to the force, it is calculated directly, and because the vector multiplication is equivalent to the vertical component, it is equivalent, and the torque is a vector.

Finally, I emphasize to give you some knowledge:

Some quantities are only scalars, not vectors, such as mass, density, temperature and energy.

Other quantities can also be vectors, but not all quantities are regarded as vectors, which depends on needs.

For example, distance class and orientation class, when considering the relative position and orientation, vector should be used when there is a vector relationship.

But you don't need to consider the direction. When you only emphasize quantity, you only need to use scalar. For example, how far a person can go and how strong a person is have nothing to do with the direction. If you have to use vectors, it will be a joke.