# Cable on a Table (classical mechanics)

bluedrew

## Homework Statement

A perfectly flexible cable has length l. Initially, the cable is at rest, with a length of it hanging vertically over the edge of a table. Neglecting friction, consider the cable's motion as it slips off the edge of the table. (a) Show that the length hanging over the edge after a time t is given by x(t) = x0cosh ($$\sqrt{}g/l$$*t
(b) Find the velocity and the acceleration of the rope as functions of time.
(c) Find the time tend from the start of the rope's slide to the moment at which the cable slides completely off the table, and
(d) the velocity and the acceleration at time tend

## Homework Equations

Assume that the sections of cable remain straight during the motion.

## The Attempt at a Solution

Clearly, the force is not constant on the whole cable and as it slides off the table, the acceleration is getting closer to g. I've written the mass per unit length as D=m/l (where m is the mass of the portion of the cable hanging over the table and l is the length of the cable), and I know for part (a) I have to solve for Dg=M*(d2x/dt2) (where g is gravity, and M is the mass of the whole cable), but I'm not sure how to do that. What does d2x/dt2 become?

Thanks so much in advance, there's something really simple I'm just not seeing here.