Finding Work using Calculus - The Cable/Rope Problem - Part b

[swabsDE]

why can't you do that all in one integral? integrate between 0 and 30 (60-x)2dx

[hallyo456]

Why cant you just use 30ft for delta x for the first 30ft as you did the last 30 ft? The change in distance for the first half is the same as the second half, is it not?

[TheAnthonySoriano]

What do you do if there is a block attached at the bottom of the rope? How do you set up the integral..?

[farazbehrouz2002]

the units of weight is just lb, not lb/ft.

other than that. great vid.

[ixionike]

@farazbehrouz2002

that's unit of weight not mass. weight is a force.

[Charounson]

Patrick, is it not slightly incorrect to use units of feet and pounds in a work problem? Force is defined to be measured in Newtons so shouldn't your units for force be in Newtons or some form of newtons (i.e. kiloNewtons..). Also, work is a form of energy so it's given in Joules so, the equation W=F*d is no longer homogeneous if you units at the end are really ft-lbs.. I don't believe Joules = ft-lbs.. It's possible that I'm completely wrong. :)

[turionking]

Question: Why aren't you multiplying the mass by the force of gravity 9.8? :)

[turionking]

@turionking And don't you have to treat the bottom section as a dead weight and not treat it as an integral?

[turionking]

I'm using the metric system if that would make a difference?

[ambdeyou]

thanks for your videos!they are always sooo helpful!

[lawmanbaseball]

if only all calculus teachers could explain stuff like you do, calculus would be much easier and less stressful

[dustinchen]

man this guy explains it a million times better than my teacher does...

[j5drumr]

wait a minute,....how does adding the W(top) and W(bottom) = W (half the rope)?

[kronikinsomniak]

@j5drumr the bottom half of the rope still has to move up, its all one piece, so you are adding the work required to move the bottom half up as well. You aren't just lifting half of the rope, but the WHOLE rope HALFWAY up.

[bluejimmy168]

Where's part A?

[patrickJMT]

@bluejimmy168 it was set to private for some reason, sorry. it is available now!

[bluejimmy168]

@patrickJMT Thank you soooo much. If you ever have time or feel like doing math, it would be so nice if you can make a video of why integral works. Like proof it. I know how to do it but just cant figure out why it works. Its like magic for me now lol. i understand riemann sum but just dont know where integral came from. Anyway thank you so much for all the great videos!!

[newpurgatory]

@bluejimmy168 if a derivative is the slope the very instant of a point then the opposite, the antiderivative, would be like adding all these infinitesimal points from a to b (The limits of Integration). all you are doing is reversing the operation of a derivative. Thus, the opposite of the slope of an instant is the total change of something. idk it just works!

[choconiel]

today ill take my test for 25B and 25C your videos helped me a lot for those 2 tests :DDD watching ur videos and reading the book, i feel that i can conquer the world hahahhahaa thanks

[patrickJMT]

@choconiel ha : ) good luck on it all!

[danlyomil]

why are you integrating the second part, from 30-60 if you're only pulling up the first half. I know it has to do with the fact that the bottom part will weigh down the top half... but i'm still a little hazy as to how we come to the equation for the bottom half.

[valsera246]

I just do not get this part...The bottom half of the rope stays aconstant, so why do we need to integrate it? Can't we just multiply 30 ft with 2 lb/ft ? nothing is changing for the bottom half, so we basically need to use Work=Force* distance....? I'm just asking because I'm kind of confused...

Thanks for your videos Patrick. I highly appreciate your help :)

[SonicGCT]

How come the Part A video is set to private??

[patrickJMT]

@SonicGCT did not know it was, it is fixed now - thanks for letting me know.

[modesforlife]

@patrickJMT . Hi, can you please post the first part to this problems it's still not working? thank you and keep the good job

[bluejimmy168]

@modesforlife hey, its on his website and i just watched it :). or copy and paste the title of this video with part A instead of b

[Bob8199]

Patrick, you're the best math tutor on Youtube.

[patrickJMT]

thanks.

just explaining things the way i understand them, is all

[patrickJMT]

@Bob8199 thanks! just tryin' my best here...

[KingCorvette]

I though that whenever you use integrals, you are finding the area under a curve. While I do think this is awesome, I am astonished at how useful something I thought was boring and bare could be.

[Cocolossal]

What the hell's all these ancient Imperial British units? How about using a system we understand.

[nickschor]

Thanks again, Patrick.

Wonderful lesson!!

I now also know WHY we do these integrals...not just how. I feel....well....smarter!

[MicroTex23]

Thanks Patrick, keep up the amazing work, awesome video

[80amnesia]

thnx

[espobulldog]

Absolutely awesome. Keep these coming please! There is such a lack of informational videos regarding the applications of calculus. These type of problems are great practice problems too.

[roflcopter2225]

awesome video

[andreiduffy]

Thank you!