(^162) A Textbook of Engineering Mechanics

and now resolving the forces vertically,

R 2 sin (15° + 14°) + 1000 = R 1 cos 14°

R 2 × 0.4848 + 1000 = R 1 × 0.9703 = (3.616 R 2 ) 0.9703 = 3.51 R 2 ...(Q R 1 = 3.616 R 2 )

or 1000 = R 2 (3.51 – 0.4848) = 3.0252 R 2

∴ (^21000) 330.6 N

3.0252

R ==

Now consider equilibrium of the wedge. We know that it is in equilibrium under the action of

the following forces as shown in Fig. 9.17. (b) :

- Reaction R 2 of the body on the wedge,
- Force (P) acting vertically downwards, and
- Reaction R 3 on the vertical surface.

Resolving the forces horizontally,

R 3 cos 14° = R 2 cos (14° + 15°) = R 2 cos 29°

R 3 × 0.9703 = R 2 × 0.8746 = 330.6 × 0.8746 = 289.1

`∴ 3`

289.1

297.9 N

0.9703

`R==`

`and now resolving the forces vertically,`

P = R 3 sin 14° + R 2 sin (14° + 15°)

= (297.9 × 0.2419) + (330.6 × 0.4848) = 232.3 N Ans.

EXERCISE 9.2

- A block (A) of weight 5 kN is to be raised by means of a 20° wedge (B) by the application

of a horizontal force (P) as shown in Fig. 9.18. The block A is constrained to move

vertically by the application of a horizontal force (S). Find the magnitude of the forces F

and S, when the coefficient of friction at the contact surfaces is 0.25.

[Ans. 4.62 kN; 3.77 kN]

`Fig. 9.18. Fig. 9.19.`

2. A block weighing 10 kN is to be raised against a surface, which is inclined at 60° with the

horizontal by means of a 15° wedge as shown in Fig. 9.19.

Find graphically the horizontal force (P) which will just start the block to move, if the

coefficient of friction between all the surfaces of contact be 0.2. Also check the answer

analytically. [Ans. 6 kN]