Finding velocity of falling object

[jubin]

A one meter chain that weighs one Newton sits on a flat horizontal table that is one meter
from the floor. The coefficient of friction between the chain and table is 0.15. How much of the chain can dangle off the table until the chain pulls itself onto the floor?If it starts to fall from this position of "maximum dangle", how fast is the chain moving when it first hits the floor

 

[Whovian]

Do you have any experience with differential equations? Because if you do, I'd suggest using one to determine "jerk" of the chain.

 

[mahnoorbloch]

yes i have an experience with differential equations.

 

[Whovian]

Set up a differential equation for acceleration in terms of how much chain's dangling off. Solve it. My previous post stands corrected, acceleration, not "jerk."

Also note that you'll have to find the maximum dangle by setting the force of the chain being pulled off equal to the force of friction. From here, I'd imagine you'd get a state of no change.

 

[jubin]

is there another way to solve this problem without using differential equations?

 

[mfb]

Looking at the energy in the system should work, if you include the friction as energy drain.

However, a real chain would rotate while falling (probably with some oscillations in addition), which makes the system much more complex as it is intended here.