# Math Help - equilibrium

1. ## equilibrium

A rod is suspended by means of two light inextensible trings attached at points D and E on the rod where AD is y metres and EB is 1m.

The sytem hangs in equilibrium with the rod horizontal
i)Fidn in terms of y and g, the tension in the string attached at D

2. Originally Posted by helpishere
A rod is suspended by means of two light inextensible trings attached at points D and E on the rod where AD is y metres and EB is 1m.

The sytem hangs in equilibrium with the rod horizontal
i)Fidn in terms of y and g, the tension in the string attached at D
Let the length of the rod be $l$, and the tension in the string at $D$ be $T_D$ and that at $E$ be $T_E$.

Now the two tensions must balence the downward gravitational force on the system so:

$T_D+T_E=5g \ \ \ \ \ \ \ \ ..(1)$

Now take moments about $E$:

$
-(l-1-y)T_D+3l-2=0 \ \ \ \ \ \ \ \ ..(2)
$

Take moments about $A$

....

Take moments about $B$

....

Now you will have four equations in the four unknowns $l, y, T_D$ and $T_E$ which you can use to solve for $T_D$

RonL