Help!

[hammerforge]

I need a second pair of eyes. I have done something for my Calculus 3 class that is either clever or utter crap, and I am unsure of which. I am on the chapter for line integrals and have the following problem: A 160 lb man carries a 25 lb can of paint up a helical staircase that encircles a silo with a radius of 20 ft. Over the course of his climb

Comments

[chamcha]

You have that nice little function of t, but no way of relating how far he has climbed to how long he has been climbing! What are you limits of integration? Try re-expressing it in terms of something you do know -- height.

[hammerforge]

Do I need time? I know that over the entire duration of the climb, a total of 9 lbs of paint has leaked out, and that his final height is 90'. What I do not know from the problem setup is what the duration of the climb was, nor the rate of ascent. I also lack initial and final volume of paint and for that matter density per volume unit. And so I have tried to eliminate any kind of time based value for leackage.

I first made the assumption that as gravity is a conservative vector, I could use a height of 0

[chamcha]

Sorry...I don't know what I was thinking. Actually I do. I was thinking your g(M + P - t/10) was a function of time. Just kidding.

So what's the problem? Integrate that with respect to distance from 0 to 90. It doesn't matter that he is also moving in a circle. Gravity doesn't effect this, as you pointed out.

[chamcha]

You're forgetting that when you integrate t/10 dt, you change dimensions. t/10 gives you the amount of paint lost, the integral of that is in lbs*feet.