Engineering Mechanics

Chapter 3 : Moments and Their Applications „„„„„ 39

Example 3.9. Find the tension required in the operating
wire to raise the signal through the system of levers as shown in
Fig. 3.17. All dimensions are in mm.

Solution. Given : Weight of signal arm (W ) = 150 N
Let T = Tension required in operating wire, and
P = Tension in wire AB.
First of all, taking moment about the fulcrum (F 1 ) of the signal
and equating the same,

P × 75 = 150 × 175 = 26 250 N-mm

∴

26 250

350 N

75

P==

Now taking moments about the fulcrum (F 2 ) of the operating
wire and equating the same,
T × 75 = 350 × 150 = 52 500 N-mm

∴

52 500

700 N

75

T== Ans.

Example 3.11. Fig. 3.18 shows a crank-lever ABC with a tension spring (T). The lever
weighs 0.2 N/mm.

Fig. 3.18.

Determine the tension developed in the spring, when a load of 100 N is applied at A.
Solution. Given : Weight of lever = 0.2 N/ mm ; Force applied on the effort arm (P) = 100 N;
Length of the effert arm (a) = 200 mm and length of the load arm (b) = 100 mm.

Let T = Tension developed in the spring.

∴ We know that *weight of the lever AB

= 200 × 0.2 = 40 N

and it is acting at the mid-point of AB i.e. 100 mm from A or B.

Taking moments about the hinge B and equating the same.

T × 100 = (100 × 200) + (40 × 100) = 24 000 N-mm

∴

24 000

24 N

100

T== Ans.

Fig. 3.17.

* The weight of lever BC will have no moment about the hinge B. Therefore its weight has been

ignored.