Square Root Practice: Multiplying by 1000NM/kJ

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The discussion centers on the multiplication by 1000 NM/kJ within a square root, which is identified as a units conversion. Participants clarify that multiplying by "1" facilitates converting between different units while maintaining the equation's integrity. There is confusion regarding the inconsistent use of symbols for meters and joules, with some expressing frustration over the lack of clarity. The use of mixed units, such as [25 + 273K], is also criticized for being misleading. Overall, the thread highlights the importance of consistent unit representation in technical discussions.
sandmanvgc
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Summary:: Why are you multiplying by 1000NM/kJ within square root?

Practice problem for FE

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sandmanvgc said:
Why are you multiplying by 1000NM/kJ within square root?
It's just a units conversion. Multiply by "1" whenever you want to convert from one set of units to another (and have the two sets of units in the numerator and denominator with appropriate multipliers to keep the fraction = 1):

$$1 = \frac{1000 N m}{1kJ}$$

Or in words, "1000 Newton-meters is equal to 1 kiloJoule" :wink:
 
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BTW, they appear to be using both "M" and "m" for meters. Or am I misinterpreting something?

1609185386665.png
 
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Yes, just as they use j and J for joules. Pure carelessness.
 
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mjc123 said:
Yes, just as they use j and J for joules. Pure carelessness.
That threw me off
 
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berkeman said:
BTW, they appear to be using both "M" and "m" for meters. Or am I misinterpreting something?

View attachment 275275

They are all over the place with units. They also have [25 + 273K] as if only the second term has units. Totally bizarre.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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