# Math Help - Uniform rod / moments

1. ## Uniform rod / moments

The diagram shows a uniform rod AB, of length 2a and weight W, resting in equilibrium with its end A on a rough horizontal floor and the end B connected to a point C on the floor by a light inextensible string. The plane ABC is vertical. The rod makes an angle of 60 degrees with the floor and the string makes an angle of 30 degrees with the floor. The coefficient of friction between the rod and the floor is mew.

a) Find, in terms of W, the magnitude of the tension in the string

b) Find the least possible value of mew.

Ok for part a i'm not sure exactly what to do but i assume you resolve vertically. So by saying the reaction of the rod on the floor is R i get

R + Tsin30 = W

but im not sure if this is right or where to go with it :/

also not sure about part b maybe something to do with when slips
F< mew*R and taking moments about A ???

2. $\sum \tau = 0$

$T\sin(30) \cdot 2a = W\sin(30) \cdot a
$

$T = \frac{W}{2}$

$\sum F_y = 0$

$W + T\sin(30) = N$

$N = \frac{5W}{4}$

$\sum F_x = 0$

$T\cos(30) = f_s$

$f_s \le \mu \cdot N$

$T\cos(30) \le \mu \cdot \frac{5W}{4}$

$\frac{\sqrt{3} W}{4} \le \mu \cdot \frac{5W}{4}$

$\mu \ge \frac{\sqrt{3}}{5}$