Reading 9
Preclass assignment due with problem set #9
Do the following problem. It was on last semester's first exam. Be ready to talk about how you did it in class. (You'll get full credit on the homework just for trying it.) On the ILT website, instead of answering what you what to discuss about the reading, tell us what is most difficult for you when you do "work" problems in general or this work problem in particular.
A rope is 10 m long and hangs over the edge of a building. It has a
5 kg piece of granite attached to one end. You are required to
pull the whole rope over the edge, pulling the granite to the top of the
building
a) Suppose the rope has a uniform density of 1 kg/m. Write an integral
that gives the amount of work required to pull the rope and the granite up to
the top of the building. Feel free to express your answer in terms of g, the
gravitational constant. You need not evaluate the integral.
b) Suppose that the rope has instead, a non uniform density given by
D(x) = 1+x^2 where x is the distance (in meters) above the granite.
Write an integral that gives the amount of work required to pull the rope and
the granite up to the top of the building. Feel free to express your answer
in terms of g, the gravitational constant. (You need not evaluate the
integral.)
Hint: You should slice the rope.