Questions about units and conversion

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When solving physics problems, it's crucial to ensure that all units are compatible to obtain the correct answer. If the problem provides non-SI units, you can use them directly as long as they are consistent with each other. For instance, if gravitational acceleration is given in feet per second squared and time in seconds, the result will be in feet. However, converting to SI units can simplify calculations and help confirm the final units. Ultimately, maintaining unit consistency is key to achieving accurate results.
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When you solve a problem and it wants the answer in non-SI units and they given you non-SI units, do you need to convert the non-SI units to SI units before you plug them into equations such as x=1/2gt^2. If you don't convert them into SI units, you'll get the answer wrong right?

Basically, all the units need to math up in order for you to get the right answer?
 
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what is g in m/s^2? how many feet are in a meter? Now, do you think you need to convert it?
 
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For something like that it shouldn't be a problem; i.e. if you are given g in ft/s2 and time in s, then x will be in ft. In general, you need to use units are compatible with each other, so you know the units of the thing you find in the end. If it's a more tricky calculation, then it may be easier to convert to the units you are familiar with (SI) to perform the calculation, so that then you know the correct units that the answr will be in, and then convert back. It's upto you.
 
ok thanks. i just came across a problem that gave non SI units and asked you to give the answer in non SI units. I forgot to convert everything to the same units =[
 
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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