Units and Constants

Before I start anything, I need to be sure that I have a pretty good idea on what are the differences between the English and SI (metric) system. The SI coming from french "Système International" is a complete system of units of measurements used internationally. mks system (based on meter, kilogram, and seconds) is included in metric system. Here is the units of the fundamental quantities in this system: length (meter, m), mass (kilogram, kg), time (second, s), electric current (ampere, A), temperature (kelvin, K), and amount of matter (mole, mol). Detailed information on these base units can be found here. On the other side the English system has been using the pound unit both for mass and force which resulted in much confusion. So what is wrong with it? The point is that mass is always constant but weight has the nature of force and changes with gravitational fields. That is, if a coffee mug weighs 1 N (Newton) on earth, it won't weight the same on the moon, It weighs about 0.2 N over there!! And it weighs about 2.5 N over on Jupiter! The SI unit for is newton which is equal to 1 kg.m/s2. 

A Wikipedia page is available for all the different types of conversions from one system to another. 

Also, Here is a nice page for playing around with the different units and how to convert them to each other.

Alright so now how do I convert mass to weight? Here is the equation for this matter:

Weight = Mass x Gravitational acceleration

W = m × g

This confirms that weight has the nature of force as from Newton's second law of motion in physics we know that force is equal to mass times acceleration. 

F = m × a

Now if the acceleration is only imposed by gravity and no external reason, I call the resulted force as weight! Neat! Beware, that whenever using an equation for calculating a parameter, both sides of the equation should follow the same system of units. In that case, we call it to be consistent (homogeneous, or coherent). 

Note. If pound-mass (lbm) and pound-force (lbf) is given in a question, the equation won't be consistent unless a conversion factor of 32.2 (lbm-ft/lbf-s2) is applied to the equation like the following. This value is not the local gravitational acceleration (g), although their numerical values are the same. This value is called gravitational constant to make the equation consistent in English system. Similar to this, there are other equations that are affected by inconsistencies in the English system of units that require a conversion factor. Some examples are the calculation of kinetic energy, pressure at depth, weight, or specific weight.

F = m × a / 32.2

W = m × g / 32.2

The gravitational acceleration on our planet is equal to 9.81 m/s2 or 32.2 ft/s2. That is because there is about 3.28 ft in every meter of length, so 9.81 times 3.28 equals 32.2. 

So why the unit for acceleration is m/s2? well the acceleration is basically the rate of the change in speed, which means how the speed of an object changes over time. And, speed itself is the rate of the change in location of an object over time. Therefore, if we consider the units, we will come up with the change of location over time as "m/s" for speed and then the change of speed over time as "m/s/s" which becomes "m/s2". There is also a mathematical realization of this rate calculations using derivatives and second derivatives. 

Now if a force is applied over some length, some work has been done. That is why they call it work. obviously, when some work is done, there has been some energy to do the work. So the units of work and energy are the same. It is called joule named after James Prescott Joule, an English physicist.

J (Joule or N.m or kg.m2/s2) = F (N or kg.m/s2) ×  L  (m)

How much energy do I spend or how much work have I done? Let's say I can lift a 5 kg bucket of water up to 2 meters high. That means I have spent 5 ×  9.81 × 2 = 98.1 N.m or Joule. Now if I ask myself how long can I hold it up there, I am questioning my power which is essentially the use of energy over time. That means, if I can hold the bucket for 30 seconds, I have a power of 98.1/30 = 3.27 joules per second or watt. So, power is basically the rate of doing work in time or rate of spending energy over time.