Finding units for power via Dimensional Analysis? Makes no sense

In summary: In that case, you would express the Newtons in terms of those units, and then use the formula Power = Work/Time, where Work = Force*Distance, and then simplify to get the final unit of kg*m^2/s^3.
  • #1
Elysian
33
0

Homework Statement



"Power is the rate at which work is performed.

Power is signified by W for watts.

Power is also the amount of energy transmitted in a unit of time (s).

Energy is measured in joules. Joules have the units of Newton∙meters.

A Newton is a unit of force. It is equal to the amount of force required to give a 1 kilogram mass and acceleration of one meter per second squared."

Using the aforementioned information, determine the units for power by completing a dimensional analysis.


Homework Equations


Down


The Attempt at a Solution



Ok so I know that the units for power are Joules/seconds.. How would you go about getting this by dimensional analysis at all?

So I've done

P = J/s

Power (P) = Work (W)/time (t)
P is in Watts (W)
Watts is J/s

Not sure at all what to do, this is worded so weirdly.. If anyone could help me see what exactly to do, that'd be appreciated.
 
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  • #2
Currently, you have done this question by working backwards. You were pretty much there.

The unit for Force is Newtons

Work = force * distance. Hence, the units for work is Newtons * distance (Nm) which is equivalent to Joules.

Now, reapply this to what you've already done and you're pretty much there.
 
  • #3
It might be asking you to get strictly down to units of kg, m, and s.
 

Related to Finding units for power via Dimensional Analysis? Makes no sense

1. What is dimensional analysis?

Dimensional analysis is a method used in science to convert units of measurement from one system to another or to check the consistency of equations by analyzing the dimensions of the quantities involved.

2. Why is dimensional analysis important?

Dimensional analysis is important because it allows scientists to easily convert units of measurement and check the validity of equations. It also helps to identify any errors in calculations and ensures the correct units are used in scientific experiments and studies.

3. How do you use dimensional analysis to find units for power?

To find units for power using dimensional analysis, you need to first identify the equation for power, which is P = W/t. Then, use the dimensions of work (W) and time (t) to determine the dimensions of power. Since work is measured in joules (J) and time is measured in seconds (s), power must have the dimensions of J/s or watts (W).

4. Can dimensional analysis be used for any type of unit conversion?

Yes, dimensional analysis can be used for any type of unit conversion as long as the equation involves quantities with known dimensions. This method is commonly used in physics, chemistry, and engineering to convert between units of measurement.

5. Are there any limitations to using dimensional analysis?

While dimensional analysis is a useful tool, it does have some limitations. It assumes that the equation is dimensionally homogeneous, meaning that all terms have the same dimensions. It also does not take into account any non-linear relationships between quantities. Additionally, it may not be applicable for very complex equations with multiple variables and units.

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