Final answer:
Work and force have different SI units because they represent different physical concepts; force is measured in newtons and work in joules, both of which are derived units involving the fundamental quantities of mass, length, and time in different combinations.
Step-by-step explanation:
The question poses a valid observation: both work and force depend upon three fundamental unit mass, length and time. However, they have different SI units because they represent different physical concepts. The SI unit of force is the newton (N), which is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared, as per the equation Fnet = ma. On the other hand, the SI unit of work is the joule (J), which is the work done by a force of one newton moving an object one meter in the direction of the force. These definitions stem from the fact that work is a form of energy transfer, and force is an interaction that causes a change in motion.
Both force and work are derived units because they are combinations of the three fundamental units: meter (m) for length, kilogram (kg) for mass, and second (s) for time. For example, the newton is derived from the fundamental units as kg⋅m/s^2, and the joule is derived as N⋅m or kg⋅m^2/s^2. This reflects the different ways these quantities interact within the framework of physics. Derived units are essential in physics as they represent more complex relationships and interactions between the fundamental quantities.