A Classical Approach of Newtonian Mechanics

10 STATICS 10.6 Jointed rods

Y 2

Figure 94: Three identical jointed rods.

reactions on one another, in accordance with Newton’s third law. Let T be the
tension in the cable.

Setting the horizontal and vertical forces acting on rod AB to zero, we obtain

X 1 − X 3 = 0, (10.36)

T + Y 1 + Y 3 − M g = 0, (10.37)

respectively. Setting the horizontal and vertical forces acting on rod AC to zero,
we obtain

X 2 − X 1 = 0, (10.38)

Y 2 − Y 1 − M g = 0, (10.39)

respectively. Finally, setting the horizontal and vertical forces acting on rod BC
to zero, we obtain

X 3 − X 2 = 0, (10.40)

−Y 2 − Y 3 − M g = 0, (10.41)

respectively. Incidentally, it is clear, from symmetry, that X 1 = X 3 and Y 1 = Y 3.
Thus, the above equations can be solved to give

T = 3 M g, (10.42)

cable

Y 1

T

X 1

A l^

Y 3

B

X^1 X^3 

X 3

Y 1

M g

Y 2



Y 3

rod (^) M g
X (^2) C
M g
X 2