Let \(x\) be the length of the rope that is hanging over the edge at a given moment in time. (a) Show that \(x\) satisfies the equation of motion \(d^2x/dt^2=gx/L\). [Hint: Use \(F=dp/dt\), which allo...Let \(x\) be the length of the rope that is hanging over the edge at a given moment in time. (a) Show that \(x\) satisfies the equation of motion \(d^2x/dt^2=gx/L\). [Hint: Use \(F=dp/dt\), which allows you to handle the two parts of the rope separately even though mass is moving out of one part and into the other.] (b) Give a physical explanation for the fact that a larger value of \(x\) on the right-hand side of the equation leads to a greater value of the acceleration on the left side. (c) W…
