Question
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.
Answers
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
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
Why do you subtract the 2 integrals?
Related Questions
What hanging mass will stretch a 1.6 meter long, 0.66cm diameter steel wire by 1.4cm.?
Need answer...
A 100.0 meter long transmission cable is suspended between two towers. If the mass density is 2.00 k...
1. A silver bar 0.125 meter long is subjected to a temperature change from 200C to 100C. What will b...
Help: A 2 meter long, uniform bar with a mass of 46 kg is suspended from a pin so it can rotate free...