A Classical Approach of Newtonian Mechanics

10 STATICS 10.4 Rods and cables

T 2

A

M g

Figure 91: A horizontal rod suspended by two vertical cables.

T =

l/2 − x 1

M g. (10.18)

(^2) x 2 − x 1
Recall that tensions in flexible cables can never be negative, since this would
imply that the cables in question were being compressed. Of course, when cables
are compressed they simply collapse. It is clear, from the above expressions, that
in order for the tensions T 1 and T 2 to remain positive (given that x 2 > x 1 ), the
following conditions must be satisfied:
x 1 <
x 2 >
l
, (10.19)
2
l

. (10.20)
2

In other words, the attachment points of the two cables must straddle the centre
of mass of the rod.

Consider a uniform rod of mass M and length l which is free to rotate in the

vertical plane about a fixed pivot attached to one of its ends. The other end of

the rod is attached to a fixed cable. We can imagine that both the pivot and the

cable are anchored in the same vertical wall. See Fig. 92. Suppose that the rod is

level, and that the cable subtends an angle θ with the horizontal. Assuming that

the rod is in equilibrium, what is the magnitude of the tension, T, in the cable,
and what is the direction and magnitude of the reaction, R, at the pivot?

x 2

x 1

l/2

T 1