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# 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. If the silo is 90 ft high and the man makes exactly three complete revolutions climbing to the top, how much work is done by the man against gravity?

## $\mathrm{mass}\cdot32 \mathrm{ft} / \mathrm{s}^{2} \cdot 90 \mathrm{ft} ~25-\mathrm{lb}$

Vector Calculus

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for this problem. I think I'm going to borrow a concept from the From the next section. That is Gravity is ah, is her conservative force field. That means he's a Grady in off some potential scaler function. If that is the case, the energy and the work down is simply the difference off the potential. Yes, I know you can go through all the process and to set up the line a pro and try to figure out Hold this up. What is, uh, actually work down on the computer half that TR likes how it did many times in our problems, but I think for these problems are necessary. The work tango simply p a difference in in potential and what is near the front. Uh, the potential energy will be just be the mass times gravity constant, which is in this unit system, is thiss on times the height, which is she's thiss as your masses. This twenty five, there was a walk down by a man. So it's actually sir the stuff he's carrying twenty five pounds, and you can you can simplify the unit and the number of further

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Vector Calculus

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