A homogeneous chain of length l lies on a table. What is the maximum length l, of the chain that can hang over the table if the coefficient of friction is µ?

Question

A homogeneous chain of length l  lies on a table.  What is the maximum length l, of the chain that can hang over the table if the coefficient of friction is µ?

anonymous · Answer

$$\mu l/(\mu +1 )$$ i think so

anonymous · Answer

The above is correct. The length is a maximum when the force due to gravity on the hanging chain just overcomes the force due to friction of the chain on the table.

F = CF . m(table) . g = m(hanging). g

mass is proportional to length do substitute for L

CF. L(t).g = L(h).g

And L = L(t) + L(h)

So CF (L - L(h)).g = L(h).g
CF.L -CF.L(h) = L(h)

L(h) = CF.L/ (1+ CF)