Calculating Acceleration Force: How Much Mass Can a Given Force Accelerate?

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To calculate acceleration force, the relationship F = ma is crucial. Given a force that accelerates 4.5 kg at 40 m/s², it can be used to determine how much acceleration that same force would provide for an 18 kg mass. By rearranging the formula, if m1 is 4.5 kg and a1 is 10 m/s², the force can be calculated as F = (4.5)(10). Using the same force for 18 kg, the acceleration can be found with the equation (4.5)(10) = (18)(a). This method illustrates the fundamental principles of Newton's second law of motion.
Gashouse
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If a force accelerates 4.5 kg at 40 m/s ^2, that same force would accelerate 18 kg how much?
 
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Force equals mass times acceleration! (F= ma)

If m= 4.5 kg and a= 10 m/s2, what is F?

Now, using that same force, but m= 18kg, solve F= ma for a.

A slightly more sophisticated method is to say m1a1= F= m2a2.

That is (4.5)(10)= (18)(a).
 
HallsofIvy

Thanks again for the instruction, that made more sense to me. Thanks in advance.
 
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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