Cost of 41kW Motor for 32 Weeks: $17,633.28

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Discussion Overview

The discussion revolves around the calculation of the cost of running a 41kW motor continuously for 32 weeks, as well as the application of similar calculations to a generator producing 1 Megawatt. The scope includes homework-related calculations and mathematical reasoning.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents a calculation for the cost of running a 41kW motor continuously, questioning if their method is correct.
  • Another participant confirms the calculation is correct but points out that the units should be clarified, explaining how the units cancel out to yield dollars.
  • A participant inquires whether a similar calculation method applies to a generator outputting 1 Megawatt, proposing a calculation for annual energy output.
  • A later reply agrees with the initial inquiry about the generator's output but notes a potential oversight regarding the "per year" specification in the calculation.

Areas of Agreement / Disagreement

Participants generally agree on the correctness of the calculations presented, but there are nuances regarding unit clarity and the specification of time in the generator's output calculation.

Contextual Notes

Some participants highlight the importance of unit cancellation in calculations, while others note the need for clarity in specifying time periods in energy output calculations.

Onoff32
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Homework Statement



If I calculate that a motor needs 41kW continuously throughout a day to run, and it costs $0.08 per kWh to run, to calculate the cost of this for 32 weeks, I would do 41 x 24hours x 7days x 32weeks x $0.08 = $17633.28

is this a correct way of working it out?
 
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Onoff32 said:

Homework Statement



If I calculate that a motor needs 41kW continuously throughout a day to run, and it costs $0.08 per kWh to run, to calculate the cost of this for 32 weeks, I would do 41 x 24hours x 7days x 32weeks x $0.08 = $17633.28

is this a correct way of working it out?
Your number is are correct, but your units don't make any sense.

Here's what you should have, including the appropriate units.
##41 kW \times 24 \frac{\text{hours}}{\text{day}} \times 7 \frac{\text{days}}{\text{week}} \times 32 \text{weeks} \times .08 \frac{$}{\text{kWh}} = $17,633.28##.
The day units cancel, the week units cancel, and the kWh units cancel, so you're left with dollar units.
41 kW times 1 hour = 41 kWh, or 1 kW times 41 hours = 41 kWh, as well.
 
Would that work for generation as well? If a generator puts out 1MegaWatt then it would follow that
1MW x 24 hours/day x 365 days/year=8,760 MWh or 8,760,000 kWH? Thank you
 
CherryB said:
Would that work for generation as well? If a generator puts out 1MegaWatt then it would follow that
1MW x 24 hours/day x 365 days/year=8,760 MWh or 8,760,000 kWH? Thank you
That's what I get, so I'll say the answer is yes.
Though a nit-picky person might say you forgot the "per year": 8,760,000 kWH per year
 
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