Dropping Beads and their velocity?

[Olive1923]

Homework Statement

A straight rope is dropped at a height where is it not touching the ground. The rope has 10 beads spaced out on it and tied so they do not move. From the bottom to the top, the space between the beads increase, where the distance is the smallest at the bottom and largest at the top. When the rope is dropped, the beads sound like they are hitting the ground at equal time intervals. Why does it sound like this and how would you find the correct distance space out the beads?

Homework Equations

I think this is a sense problem not a math problem, so no equations needed.

The Attempt at a Solution

I think for finding the distance, you have to space it out enough so that the velocity of the top bead has enough time to increase to match the speed of the bead below it. I am just not sure about my thoughts?

 

[billy_joule]

Equations are required..

If the time taken for the first bead to hit the ground is ## t_1 ## then the time taken for the nth bead to hit the ground is ## t_n = nt_1
##
From there we can form an expression using SUVAT equation/s for the distance between any two beads ## t_n ## and ##t_{n+1}##

 

[Olive1923]

@billy_joule What are SUVAT equations?

 

[jbriggs444]

@billy_joule What are SUVAT equations?

Equations of motion. The acronym is from some conventional variable names, S for displacement, U for initial velocity, V for final velocity, A for acceleration and T for time. Under an assumption of constant acceleration, there are "SUVAT" equations that allow each variable to be found in terms of the others. Google is your friend.