a one meter chain that weights one newton sits on a flat horizontal table that is one meter from the floor. the coefficient of friction between the chain and the 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.
m is the mass of the chain, x is the length of the dangling part.
The equation of the motion of its part that is on the table is
m•a = T – F(fr),
Tension is equal to the gravity of dangling part
T = m•g•x/L,
friction force is
F(fr) = k•N = k•m•g•(L-x)/L.
m•a = m•g•x/L - k•m•g•(L-x)/L
a = g•x/L - k•g•(L-x)/L,
The chain begins to move when a 0.
Let a =0.
x= kL/k+L = 0.15•1/(1+0.15) = 0.13.