1. The problem statement, all variables and given/known data A flexible rope of length 1.0 m slides from a frictionless table top. The rope is initially released from rest with 30 cm hanging over the edge of the table. Find the time at which the end of the rope left on the table will reach the end of the table (basically when the length of the rope hanging of the table will be the whole 1 m. This is problem 9-21 in Thornton/Marion's Classical Dynamics). 2. Relevant equations Let L be the total length of the rope and x be the portion hanging off the table. 3. The attempt at a solution I started off with [tex]dp/dt = mg x/L[/tex] because only the part hanging off the table is accelerated due to gravity. I then rewrote that as [tex]dp=mgx/L \:dt[/tex]. Since the initial momentum is zero [tex]dp=p(t)-p(0)=p(t)=mdx/dt \:dt[/tex] where t is just some later time. So I'm stuck at [tex]dx/dt=gx/L \:dt[/tex]. I can integrate over position but I'll have this (dt)^2 term that I don't know what to do with.