A rope is tied to a tree branch so that the part hanging fro

A rope is tied to a tree branch, so that the part hanging from the tree has mass M and length L. The rope has uniform density. Find the tension in the rope T(x), as a function of the distance x from the bottom of the rope. Verify that your answer makes physical sense at the bottom of the rope (x=0) and the top of the rope (x = L).

Solution

tension T= (M/L)xg , because we know T=mg here m= (M/L)x

here x is the distance from the bottom, g is gravitational acceleration

this is the formula for tension, which is a function of distance x from the bottom of the roap.

at the bottom of the roap T=0, because x=0

at the top of the roap T=Mg. here M is the mass of roap.