- #1
JTemple
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Homework Statement
Part 1: A 160lb man carries a 25lb paint can up a spiral staircase, which has radius 20 feet, completes 3 revolutions, and has final height 90 feet. What is the work done?
Part 2: This time, the man's paint can leaks at a constant rate such that he loses 9lbs of paint from bottom to top.
Homework Equations
I know that the integral of Force F along curve C has a couple equations.
Integral of...
F[tex]\bullet[/tex]dr
F[tex]\bullet[/tex]Tds
F(r(t))[tex]\bullet[/tex]r'(t)dt
The Attempt at a Solution
I tried to make a parametrization but got stuck on that for part 1. So I just used that Work is Scalar product of F and Dispacement vectors.
This gave me 185lb x 90 feet x sin(90) because he goes vertical 90 feet from where he started. The path he takes t get there is irrelevant.
Part 2 is where I'm having trouble.
I've made equations for r(t) (I think)
(Note, pi is being multiplied, not raised as an exponent)
x = 20 cost
y = 20 sint
z = 15t/[tex]\pi[/tex]
t[0, 6[tex]\pi[/tex]]
The force he has to apply at a given t has to change because he's losing paint.
F(0) = 185
F(6[tex]\pi[/tex]) = 185 - 9 = 176
F(t) = 185 - 9t/6[tex]\pi[/tex]
I know now that I'm going to have to do an integration, but I'm not sure if what I've done is right, for I have an F(t), not F(r(t)) or F(x,y,z). Any help would be appreciated :)