Posted by **Em** on Saturday, February 19, 2011 at 4:22pm.

A uniform chain of total mass m is laid out straight on a frictionless table and held stationary so that one-quarter of its length, L = 1.79 m, is hanging vertically over the edge of the table. The chain is then released. Determine the speed of the chain at the instant when only one-quarter of its length remains on the table.

- Physics -
**drwls**, Saturday, February 19, 2011 at 4:32pm
The easy way to do this is with conservation of energy, since you have to deal with an increasing acceleration rate, which would make the equation of motion rather messy. You can use energy conservation because it is frictionless.

When it starts out, the center of mass of the chain is (1/2)*(L/4) = L/8 below the table surface.

When 1/4 of the chain's length remains ion the table, the center of mass is

(1/2)(3L/4) = 3L/8 below the table surface. The change in CM height is L/4. At that time, the velocity V is given by

M g L/4 = (1/2) M V^2

g L = 2 V^2

V = sqrt(gL/2) = 2.96 m/s

- Physics -
**bobpursley**, Saturday, February 19, 2011 at 4:46pm
LEt total mass be m

force pulling: masshanging over *g

force puling: mg*x/1.79 where x is the amount hanging over.

well, then force pulling is linear with the length hanging over, so the average force between .25x and .75 x is at .5x

or avg force= mg/2

Vf^2=Vi^2+2ad

Vf^2=0+2(avgforce/m)(1/2 1.79)

Vf= sqrt (g*1.79/2)

check my thinking.

Vf= sqrt (2*

- Physics -
**bobpursley**, Saturday, February 19, 2011 at 4:47pm
ignore the last line,old typo. I agree with drwls, it is the same argument.

## Answer this Question

## Related Questions

- Physics - A chain is held on a frictionless table with 1/3 of its length hanging...
- Physics - One-fourth of length L is hanging down over the edge of a frictionless...
- physics - A chain of length l and mass ë per unit length is fully open and is ...
- Physics - a heavy metal chain of mass 0.60kg hangs over the edge of a table a)...
- Newton's law - 7. A uniform flexible chain of length l, with weight per unit ...
- Physics - A large uniform chain is hanging from the ceiling, supporting a block ...
- Physics - Masses 15 kg and 8 kg are connected by a light string that passes over...
- Science: Physics and Chemistry - I was given a systems equation. Two masses are ...
- physics - A 5 ft chain is sitting on a table with 2 ft hanging off (3 ft sitting...
- Science: Physics and Chemistry - Can someone please help me with this??? I was ...