why the unit of work and energy are equal?

The unit of work and energy can be the same because work and energy are interrelated concepts. Work is defined as the transfer of energy caused by the application of force through a displacement. Energy, on the other hand, is the capacity to do work.

The unit of work and energy in the International System of Units (SI) is the joule (J). This unit is derived from the fundamental units of mass, length, and time. One joule is defined as the amount of work done when a force of one newton is applied over a distance of one meter.

To understand why the unit of work and energy are equal, we can examine the basic formula for work: Work (W) = Force (F) x Distance (d) x cosine(theta), where theta is the angle between the force and the direction of displacement.

If we consider a force of one newton applied over a distance of one meter, the equation simplifies to W = 1 N * 1 m * cos(theta). Since the cosine of any angle between 0 and 180 degrees is always between -1 and 1, the work done will be equal to 1 J.

Similarly, energy is defined as the capacity to do work, so if a certain amount of work is done, it corresponds to a specific amount of energy being transferred. Therefore, the unit of work and energy are equal.

In summary, the unit of work and energy are equal because work is the transfer of energy, and both concepts are quantified using the same unit, the joule (J).