ENGINEERING MECHANICS GATE PI PAPER TECHNICAL SECTION PART 2

quilibrium of colinear forces: Equilibrium law: Two forces can be in equilibrium only if they are equal in magnitude, opposite in direction and collinear in action. (Tension) (Compression) Superposition and transmissibility Problem 1: A man of weight W 712 N holds one end of a rope that passes over a pulley vertically above his head and to the other end of which is attached a weight Q 534 N. Find the force with which the man's feet press against the floor

Co 712N.

Resolution ot a force Replacement of a single force by several components which will be equivalent in action to the given force is called the problem of resolution of a force. By using parallelogram law, a single force R can be resolved into two components P and Q intersecting at a point on its line of action. fp C. 2

Equilibrium of collinear forces: Equilibrium law: Two forces can be in equilibrium only if they are equal in magnitude, opposite in direction and collinear in action Law of superposition . The action of a given system of forces on a rigid body will no way be changed if we add to or subtract from them another system of forces in equilibrium

Problem 3: Two spheres of weight P and Q rest inside a hollow cylinder which is resting on a horizontal force. Draw the free body diagram of both the spheres, together and separately

. Problem 4: Draw the free body diagram of the figure shown below 25 2- Ly

Problem 5: Determine the angles a and shown in the figure 445 4156 762m dk 915) = 3947, tan-1 ( .)-51.19, a-tan-1 -tan-1 (2 2) 76251 19 51 19' 610

Equilibrium of concurrent forces in a plane If a body known to be in equilibrium is acted upon by several concurrent, coplanar forces, then these forces or rather their free vectors, when geometrically added must form a closed polygon. VThis system represents the condition of equilibrium for any system of concurrent forces in a plane. RA VRaw tan a

.Lami's theorem . If three concurrent forces are acting on a body kept in an equilibrium, then each force is proportional to the sine of angle between the other two forces and the constant of proportionality is same. 13 P OR sin sin sin Ra sin(180- ) sin 90 sin(90+ )

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Indira Roy

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Durga Singh

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