Engineering Mechanics

Chapter 3 : Moments and Their Applications „„„„„ 41

Fig. 3.20. Compound levers
A little consideration will show, that in a compound lever, the mechanical advantage (or
leverage) is greater than that in a simple lever. Mathematically, leverage in a compound lever
= Leverage of 1st lever × Leverage of 2nd lever × ...
The platform weighing machine is an important example of a compound lever. This machine
is used for weighing heavy loads such as trucks, wagons alongwith their contents. On smaller scales,
these machines are used in godowns and parcel offices of transport companies for weighing
consignment goods.
Example 3.13. A compound lever shown in Fig. 3.21 is required to lift a heavy load W

Fig. 3.21.

Find the value of W, if an effort (P) of 100 N is applied at A.

Solution. Given : Effort, (P) = 100 N

From the geometry of the lever, we find that the leverage of the upper lever AB

1

1

175

7

25

AF

BF

=== ...(i)

and leverage of the lower lever CF 2

2

2

275 25

12

25

CF

DF

+

== = ...(ii)

∴ Total leverage of the compound lever

= 7 × 12 = 84 ...(iii)

We know that the total leverage,

84

100

WW

P

==

∴ W = 100 × 84 = 8400 N = 8.4 kN Ans.

EXERCISE 3.2

1. An oil drum of 500 mm diameter and 1.5 long is to be rolled across a footstep of 100 mm
   high. Find the minimum push required at the top of the drum. Take density of the oil as
   1 kg/litre. Neglect weight of the drum. [Ans. 1444.5 N]


2. Three forces equal to 3P, 5P and 7P act simultaneously along the three sides AB, BC,
   and CA of an equilateral triangle ABC of side a. Find the magnitude, direction and
   position of the resultant once. [Ans. 3.46 P; 210° ; 1.25 a]