Need help tonight- Integration Buoyancy Problem

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The problem involves calculating the work required to push a 4 cm diameter cylinder 10 cm deeper into water. The integral used for the calculation was set up correctly, leading to a result of 0.0615 J. However, the book's answer of 0.615 J was identified as a typo, confirming that the original calculation was accurate. The discussion highlights the importance of verifying textbook answers against personal calculations. Overall, the participant successfully resolved the integration buoyancy problem and clarified the discrepancy with the textbook.
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1. Homework Statement
A 4 cm diameter cylinder floats in the water. How much work must be done to push the cylinder 10 cm deeper into the water?


2. Homework Equations



3. The Attempt at a Solution

I did the integral from 0 to .1 m of (.02m)^2 * pi * (1000kg/m^3) * (9.80) * x dx

= (12.3 x^2)/2 evaluated from 0 to .1 = .0615 J. However, the back of my book says .615 J. Somehow I ended up a decimal place off. Could someone help me?
 
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Ok, so I found out the book had a typo in it, and my answer was correct.
 
I'd say that you are right and the book is wrong.

(Oops... too late! You must have posted while I was distracted in mid post.)
 
Last edited:

Thread 'Magnitude of buoyant force in fluids of different densities'

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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