Derived Energy SI Units: UNIZOR.COM - Physics4Teens - Units in Physics -...

Notes to a video lecture on http://www.unizor.com

For a short introduction to the International System of units (SI) see the previous lecture "SI Intro & Time" within this topic.

Energy Units

All SI units used in the science of Energy are derived from base units introduced in the previous chapter Base SI Units of this part Units in Physics of the course.


Work

In a simple case of a constant force F accelerating an object along a straight line in the direction of the force the amount of work W done by this force can be measured by a product of the magnitude of a force by a distance s it pushed an object
W = F · s

This simple case is the base for introduction of a unit of work joule (J) as an amount of work done by a force of 1 newton (N) on a distance of 1 meter (m)
1 J = 1 N·m
or, using only the base SI units with 1N=1kg·m/s²,
1 J = 1 kg·m²/s²

In a more complicated case of a force acting at an angle to a trajectory we represent a vector of force as a sum of two vectors, one parallel to a trajectory and another perpendicular to it.
The component of a force that goes parallel to a trajectory is the one that does the work, while a perpendicular to it component does not move an object along a trajectory and does not work towards this movement.

So, to calculate the work performed by such a force, we use only its projection F_traj onto a trajectory that can be expressed in terms of a full magnitude of a force F and an angle φ between the vector of force and direction of a movement
F_traj = F· cos(φ)

This complication does not change the fact that work can be measured in joules defined above. Work in joules is still a product of a force along a trajectory in newtons by a distance in meters.


Power

Power is an amount of work done in a unit of time.
The unit of measuring power in SI is joules per second. This unit is called watt and one watt (W) is a joule (J) per second (s)
1 W = 1 J/s
or, using only the base SI units with 1J=1kg·m²/s²,
1 W = 1 kg·m²/s³


Energy

Let's talk about mechanical energy here.
When object X exerts a force moving another object Y, changing its position, direction or speed, thus performing some work, we say that object X has spend certain amount of energy by forcing object Y to move.

The amount of energy spent is, by definition, exactly the amount of work performed.
Therefore, an amount of energy can be measured in SI in exactly the same units as an amount of work, that is in joules (J).

In the Energy part of this course we introduced a concept of energy manifested not only in mechanical movement, but also in chemical reactions, heat, electromagnetism, gravitation, nuclear reactions etc.
All these types of energy can still be measured in joules because at the very base level we still deal with some forces and movements caused by them.