Calculus Work Pump Water From an Inverted Cone

[@faithbulger4796]

Wow thank you! I have yet to hear this problem explained so concisely, you are incredible!

[@crowsmathclass]

Thank you. Glad it helped.

[@bankscj32]

Two To TEAN Thanks for the slow and thorough explanation!!

[@crowsmathclass]

You're welcome. Glad the video helped.

[@heliossol8375]

3 years later, and this video is still helping people out. Thank you!

[@crowsmathclass]

You’re welcome. Glad it helped.

[@theweirdsquid]

Thank so much, this video was super helpful! You explained everything really well!

[@crowsmathclass]

Thank you. Glad it helped.

[@davelevison7252]

I'm not understanding why the integral would be from 2 to 10 rather than 0 to 8 if all the water is being pumped out.

[@crowsmathclass]

It’s from water closest to the top which is 2 to water farthest from top which is 10.

[@aaroncroft7514]

Anyone else get ASMR vibes from his voice 😂 Great video!

[@crowsmathclass]

Thank you.

[@tawfiqabuaita]

Why did you multiply the weight by x and dx. Isn't the formula of the work just equal to the integral of force times dx? why did you multiply by x?

[@crowsmathclass]

It’s the distance.

[@XoIoRouge]

I'm given a similar problem but in US units. It states the liquid weighs 29 pounds per cubic foot. I've replaced the 1000 in the equation with 29, and replaced the gravity from 9.8 to 32.2; everything else is the same, but my answer is wrong. Are there other steps for dealing with non-metric units?

[@crowsmathclass]

Don’t include the 32.2. Below is a video I did similar to what you are asking. kzbin.info/www/bejne/mnnaXpJroL2UhKM

[@leonardocaballero1233]

When multiplying the mass with acceleration to find the force, why was the acceleration of gravity used? Do we always use that value for these types of questions?

[@crowsmathclass]

Because it’s in metric.

[@peacethroughquestion1057]

Im not workimg in kg per m. I did the same problem for a parallelogram tank and never had to use 9.8 constant. I just used f=pv = density x volume, the dw=f x distance whwre distance equals height minus y (or x, whatever)

[@crowsmathclass]

👍

[@josephmother3589]

Thank you so much

[@crowsmathclass]

You’re welcome.

[@jeminskiiiI]

very seductive voice