Calculus

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A 20 meter long steel cable has density 2 kg per meter. It is hanging straight down. There is a 100 kg bucket of concrete attached to the bottom. How much work is required to lift the bucket 10 meters by lifting the cable ten meters? Gravitational force equals 9.8 in this problem. I tried to do the integration, separately for the top half and bottom half of the rope, but it didn't work.

  • Calculus -

    hanging mass = 100 + 2 x

    F = g(100+2x)

    do dW = F dx from x = 0 to x = 20

    W = g (100 x + x^2) at 20 - at 0
    = g (2000 + 400)
    = g (2400) = 23520 Joules

    then from x = 0 to x = 10
    g (1000 + 100) = 1100 g = 10780 Joules

    subtract I get 12740 Joules

  • Calculus -

    Why do you subtract the 2 integrals?

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