How to prove that the unit of power if derived unit?
Answers
Answer:
All other SI units are derived by multiplying, dividing or powering the base units in various combinations, For example:
mechanical work is force applied multiplied by distance moved and has the unit newton metre written as Nm.
speed is distance divided by time and has the unit metre per second written as ms.
Explanation:
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Answer:
Because there exists an organization called the General Conference on Weights and Measures (known as CGPM from its French initials), established 1875 by international agreement, which has been assigned the task to decide which units will be fundamental and which will be derived, and how those units shall be defined.
The scientists making up the body of this organization, decided that the relevant to power fundamental units shall be:
- The meter (m) for length
- The kilogram (kg) for mass
- The second (s) for time
From those units, the derived unit of force is defined, as the force which imparts to the unit of mass the unit of acceleration. It was given the name newton (N).
1 N = 1 kg∙m∙s⁻²
From this, the derived unit of energy (or work) is defined, as the work produced when the unit of force causes a displacement equal to the unit of length of its point of application along its direction. It was given the name joule (J).
1 J = 1 N∙m = 1 kg∙m²∙s⁻²
Power is, as is well known, energy per time. So, the unit of power can't be other than one unit of energy being produced every single unit of time, or 1 joule per second. (J/s). It has been given the name of watt (W). Its dimensions consequently are:
1 W = 1 J∙s⁻¹ = 1 kg∙m²∙s⁻³
I hope this explains not only why is the unit of power a derived unit, but also how it is derived.
Explanation: