calculating work by using integral, pumping water out of a tank, calculus 2 tutorial

Application of integration. Calculating the work it needs to pump the water out of a conical tank. Calculus 2 tutorial.

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#blackpenredpen #math #calculus #apcalculus

[joseumanawills]

Love his enthusiasm when teaching and explaining step-by-step process (like using the point-slope form rather than using slope-intercept form)

[timehrensberger]

You manage to make this problem easily comprehensible for a highschool student knowing only the basics of calculus. Compliments!

[mariobezrukovs]

Thanks! You made it look a million times easier than my calc 2 professor thank you!

[feezy]

Why is it so easy when you watch videos but so hard when doing homework or a test? :(

[ChaosPod]

I think saying you need to multiply the density by 9.8 is still confusing.
Here is how I would have said it:
work done (joule, J) = distance (metre, m) x force (newton, N)
F (force) = m (mass) * a (acceleration) in this case the acceleration is gravity so
Fw (weight) = m (mass) * g (gravity, 9.8 m/s^2)
Fw = m * 9.8 m/s^2.
Mass = Density x Volume

Then I would have put them together:
W=dF=d(gm)=dg(Density x Volume) where g = 9.8

[ZipADeeeDoooDaaa]

I just wanted to share this. I found a surprisingly simple formula for this problem.
W = F * (H - 3/4*h), where H = 10, h = 8
and of course
F = m * g, where m is the mass of the water and g = 9.8

Calculating the mass of the water is a bit tricky. We need the Volume of the water cone and the density of water.
V = 1/3 * π * r^2 * h
The mass of the water is about m = 85786.42 kg

Plugging all the numbers into the formula above gives you
W = 3362828 Joules

[thespicymeatball]

work = 3362827.80 joules
love your videos so much keep up the good work. Maybe i can be first this time last video i was second by a minute

[scharpmeister]

This man swaps his pens with absolute STEEZ

[AarmOZ]

Thanks to graphing calculators being able to solve definite integrals, the set up is the most important part to getting the problem right. Thanks for helping this old guy who is taking Calc II online. :)

[pythagoras]

sir you don't know how much u helped me. i couldn't sleep for 2 nights to get a proper theory on this topic. i was so close and now i completely understand this. thank you so much from the core of my heart.

[GhostyOcean]

Good job on correcting and explaining your mistake! This is how I see it: units like Lbs already have the force of gravity factored into them while SI needs to be multiplied by the force of gravity because mass is a measurement of how much matter is there. For example: something that weighs 100lbs on Earth does not weigh 100lbs on the moon, but the mass of the object stays the same.

[louisthurston]

Correct language is "work done against gravity." The pumping process will necessarily eject the fluid with some KE and there will be some viscous or thermal effects. If you only apply an upward force equal to the weight of a fluid element, it will not move. You must apply a larger force to accelerate it giving it KE.

[jaggysmf]

Currently taking Calc II, I could not understand this whatsoever from my textbook, this video makes the concept so clear. Thank you.

[MarioManiac]

W is approximately equal to 3.36 x 10^6 J.

[picorrow]

Beautifully crafted video! The bunny allowed me to ease into the complication. :)

[jamesleroy]

Thanks! This may be way late as far as a comment is concerned, but this helped me tremendously!

[Smokeybear]

I'm surprised, this really helped me understand how to do this problem a lot better. You earned a sub :)

[jesusreignonhigh]

Nostalgia. In college we were advised to use trig functions on the x, y relation for the conic shape.

[noelforde]

Couldn't you have gotten the radius with similar triangles? Or does it not work for all work problems?

[tonilynn]

I have a couple of questions. This example assumes a constant force, correct? So what if the force is NOT constant? Another question is what if we "tip" the cone and it's inclined?