Engineering Mechanics

Chapter 16 : Virtual Work „„„„„ 359

EXERCISE 16.2

1. The diameter of the pulleys in a differential pulley block are 300 mm and 250 mm
   respectively. Using the principle of virtual work and neglecting friction, find the value of
   the effort required to lift a load of 3 kN. (Ans. 250 N)


2. A block of weight (W) rests on the smooth surface inclined at 20° with the horizontal.
   The block is supported by an effort (P) hung from a pulley as shown in Fig. 16.24.

Fig. 16.24.

Using the principle of virtual work, obtain expression for (P) in terms of (W), when the

system is at rest. (Ans. P = 0.685 W)

[ Hint.

Let x = Virtual vertical upward displacement of the load W, and

y = Virtual vertical downward displacement of the effort (P)

∴ Distance through which the load (W) moves along the inclined plane

2.92

sin 20 0.3420

xx

===x

°

...(i)

and distance through which the effort (P) will move

2.92 1.46

2

x

==x ..(ii)

∴ Virtual work done by the weight (W)

= + W x

and virtual work done by the effort (P)

= – P × 1.46 x = – 1.46 Px

∴ Wx – 1.46 Px = 0 or P =

1.46

W

= 0.685 W Ans.

3. Two weights W 1 and W 2 are resting on two smooth planes AB and BC at angles of θ 1 and
   θ 2 as shown in Fig. 16.25.

Fig. 16.25.

With the help of principle of virtual work, find the ratio of W 1 and W 2.

12

21

Sin

sin

W

W

⎛⎞θ

⎜⎟=

⎝⎠θ

Ans.