calculus

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A 160-lb man carries a 25-lb can of paint up a helical staircase that encircles a silo witha radius of 20 ft. If the silo is 90 ft high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top?

I looked at this problem and got that the vector field was conservative. I've asked my tutor if this was correct and she said it "seemed" like it. My question is how does the path taken not matter? The man isn't just cutting straight up the helix to reach the top right?

Wouldn't the stairs make the distance to the top longer for the man?

please answer.

  • calculus -

    never mind. i thought about it and it is the work done by gravity. not the man. which leads me to another question. how exactly would you find the work done by the man. would he be represented as another vector or or in the vector field?

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