What is the unit for work done?

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Solution 1

J (joule) is a derived unit for energy (or work done) named after the physicist James Joule. Since $W = F.d$, we have 1 J=1 Nm. We can also express in terms of basic SI units, yielding us

1 J = 1 kg m$^2$s$^{-2}$.

Solution 2

The unit you should use for work done and energy is the joule (J) which is indeed the same as the newton metre (N m).

There is another physical quantity which is the product of force and distance and that is torque or moment of a force.
The unit you should use for torque is the newton metre (Nm) and not the joule.

Naming the units of work done and torque differently helps to emphasis the fact that work done and torque refer to two different physical quantities although the definitions of both quantities have the product of force and distance in them.

$\text{work done}= \vec{\rm force} \,\cdot\, \vec{\rm displacement} $ and $\vec {\rm torque}= \vec{\rm force} \,\times\, \vec{\rm displacement} $

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Updated on June 09, 2020

Comments

  • MythicalCode_
    MythicalCode_ over 3 years

    My textbook's equation for work done is:

    work done = force * distance

    So this means that the unit should be Nm. However, when I researched on Google, a lot of people were saying that the unit is J.

    • Abhay Hegde
      Abhay Hegde over 5 years
      Joule is a derived unit for energy (or work done). $1 J = 1 Nm = 1 kgm^2s^{-2}$
    • MythicalCode_
      MythicalCode_ over 5 years
      Oh, I didn't know that. Text books have all the complex stuff, but they miss out small stuff like this ._.
    • MythicalCode_
      MythicalCode_ over 5 years
      @JustCurious What is 1kgm2s-2 (don't know how to use superscript yet)
    • Abhay Hegde
      Abhay Hegde over 5 years
      Newton is the unit of force. $F = ma$. Expressing $1N$ in terms of basic SI units, we have $1kgms^{-2}$. Hence, $1Nm = 1kgm^2s^{-2}$.
    • MythicalCode_
      MythicalCode_ over 5 years
      @JustCurious Can you answer this question so I can accept it?
    • Jasper
      Jasper over 5 years
      Units of derived quantities are always computed from the units of the base qusntities. Sometimes they get a new fancy name, usually after a scientist.
    • Triatticus
      Triatticus over 5 years
      Thats odd, every physics textbook I have seen defines the joule as a newton meter.
    • MythicalCode_
      MythicalCode_ over 5 years
      @Triatticus Maybe I didn't search through it hard enough, it's probably hiding in the pages the teacher hasn't covered yet :P
    • Triatticus
      Triatticus over 5 years
      Perhaps, I would honestly be more than a little surprised, but indeed others have still answered your inquiry and laid you troubles to rest.
  • Philip Wood
    Philip Wood over 5 years
    Typographical conventions… Use italics for algebraic quantities, but upright (roman) for units. If you type the name of the unit in full, it starts with a small letter, even if it's named after someone. When you abbreviate the unit, the first letter of the abbreviation goes to a capital. Examples: joule abbreviated to J, hertz abbreviated to Hz.