(^76) A Textbook of Engineering Mechanics
- A ladle is lifted by means of three chains each 2 m in length. The upper ends of the chains
are attached to a ring, while the lower ends are attached to three hooks, fixed to the ladle
forming an equilateral triangle of 1.2 metre side as shown in Fig. 5.34.
Fig. 5.34.
If weight of the ladle and its contents is 5 kN, find tension in each rope. [Ans. 1.78 kN]
Hint. First of all locate the point G of the equilateral triangle ABC. Now consider the
right angled triangle AOG and resolve the forces vertically.- A spherical ball, of weight W, rests in a triangular groove whose sides are inclined
at angles α and β to the horizontal. Find the reactions at the surfaces of contact.
If a similar ball is now placed, so as to rest above the first ball, one side of which is
inclined at angle α, find the reaction of the lower ball, on the surface inclined at an
angle β.
sin sin 2 sin
;;
sin( ) sin( ) sin( )
⎡⎤WW Wα β α
⎢⎥α+β α+β α+β
⎣⎦Ans.QUESTIONS
- Enunciate any two principles of equilibrium.
- State and prove Lami’s Theorem.
- Show that if three coplaner forces, acting at a point be in equilibrium, then, each force is
proportional to the sine of the angle between the other two. - What are different methods of studying the equilibrium of coplaner forces? Describe any
one of them. - How would you find out the equilibrium of non-coplaner forces?
- Explain the conditions of equilibrium.
- Discuss the various types of equilibrium.
OBJECTIVE TYPE QUESTIONS
- According to Lami’s Theorem, the three forces
(a) Must be equal.
(b) Must be at 120° to each other.
(c) Must be both of above.
(d) May not be any of the two.